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Random Process and Linear Algebra (MA3355) - Anna University

Course Instructor Promath

₹999.00 ₹1999.00 50% OFF

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Course Overview

Schedule of Classes

Course Curriculum

6 Subjects

Unit - I : Probability and Random Variables

131 Learning Materials

1.1 Probability and Random Variable

1.1.1 Introduction of Probability

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1.1.2 Set definitions

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1.1.3 Operations on sets

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1.1.4 Laws of algebra of sets

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1.1.5 Experiments and sample spaces

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1.1.6 Discrete and Continuous sample spaces

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1.1.7 Events

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1.1.8 Probability Definitions and axioms

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1.1.9 Theorems on probability

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1.1.10 Exercises

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1.2 Mathematical model of experiments

1.2.1 Mathematical (or) classical definition of probability

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1.2.2 Solved Problem 1

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2:31
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1.2.3 Solved Problem 2

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2:18
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1.2.4 Solved Problem 3

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2:34
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1.2.5 Solved Problem 4

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2:00
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1.2.6 Solved Problem 5

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1.2.7 Mathematical tools

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1.2.8 Solved Problem 1

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4:31
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1.2.9 Solved Problem 2

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1.2.10 Solved Problem 3

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1.2.11 Exercises

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1.3 Joint probability

1.3.1 Joint Probability

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1.3.2 Introduction to Probability as Relative Frequency

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1.3.3 Solved Problem 1

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1.4 Conditional probability

1.4.1 Introduction of conditional probability

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1.4.2 Solved Problem 1

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4:9

1.4.3 Solved Problem 2

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4:34

1.4.4 Solved Problem 4

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1.5 Total probability and baye's theorem

1.5.1 Theorem of Total Probability

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1.5.2 Baye's theorem

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1.5.3 Solved Problem 1

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8:10

1.5.4 Solved Problem 2

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9:48

1.5.5 Solved Problem 3

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1.5.6 Solved Problem 4

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1.5.7 Solved Problem 5

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1.5.8 Solved Problem 6

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1.5.9 Exercises

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1.6 Independent Events

1.6.1 Independent Events (multiplication law of probability)

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1.6.2 Solved Problem 1

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1:31

1.6.3 Solved Problem 2

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2:1

1.6.4 Solved Problem 3

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3:30

1.6.5 Solved Problem 4

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1.6.6 Solved Problem 5

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5:00

1.6.7 Exercises

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1.7 Random Variable

1.7.1 Introduction of Random variable

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1.7.2 Definition of Random variable

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1.7.3 Discrete continuous and mixed random variable

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1.7.4 conditions for a function to be a random variable

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1.7.5 Probability distribution function

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1.7.6 Probability of mass function

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1.7.7 Probability of discrete random variable

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1.7.8 Solved Problem 1

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9:52

1.7.9 Solved Problem 2

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3:55

1.7.10 Solved Problem 3

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1.7.11 Solved Problem 4

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5:32

1.7.12 Solved Problem 5

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1.7.13 Exercises

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1.8 Continuous Random Variable

1.8.1 Probability distribution function

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1.8.2 Probability density function

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1.8.3 Probability of continuous random variable

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1.8.4 Solved Problem 1

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3:17

1.8.5 Solved Problem 2

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7:59

1.8.6 Solved Problem 3

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7:7

1.8.7 Solved Problem 4

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1.8.8 Solved Problem 5

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1.8.9 Solved Problem 6

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1.8.10 Exercises

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1.9 Binomial distribution

1.9.1 Introduction to binomial Distribution

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1.9.2 Mean of binomial distribution

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1.9.3 Variance of binomial distribution

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1.9.4 Moment generating function

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1.9.5 Solved Problem 1

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11:5

1.9.6 Solved Problem 2

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9:24

1.9.7 Solved Problem 3

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6:27

1.9.8 Solved problem 4

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1.9.9 Solved problem 5

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1.9.10 Solved problem 6

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1.9.11 Solved problem 7

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1.9.12 Solved problem 8

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1.9.13 Exercises

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1.10 Poisson distribution

1.10.1 Introduction to poisson distribution

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1.10.2 Mean of poisson distribution

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1.10.3 Variance of poisson distribution

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1.10.4 Moment of generating function

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1.10.5 Properties of poisson distribution 1

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1.10.6 Properties of poisson distribution 2

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1.10.7 Solved Problem 1

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6:28

1.10.8 Solved problem 2

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7:2

1.10.9 Solved Problem 3

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8:28

1.10.10 Solved Problem 4

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1.10.11 Solved Problem 5

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1.10.12 Solved Problem 6

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1.10.13 Solved Problem 7

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1.10.14 Solved Problem 8

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1.10.15 Exercises

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1.11 Geometric Distribution

1.11.1 Introduction to Geometric Distribution

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1.11.2 Solved Problem 1

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4:39

1.11.3 Solved Problem 2

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9:6

1.11.4 Solved Problem 3

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5:15

1.11.5 Solved problem 4

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1.11.6 Solved problem 5

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1.11.7 Solved problem 6

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1.11.8 Solved problem 7

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1.11.9 Solved problem 8

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1.11.10 Exercises

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1.12 Uniform distribution

1.12.1 Introduction to uniform distribution

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1.12.2 Moment generating function of uniform distribution

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1.12.3 Solved Problem 1

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8:23

1.12.4 Solved Problem 2

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3:35

1.12.5 Solved Problem 3

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9:26

1.12.6 Solved Problem 4

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1.12.7 Exercises

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1.13 Normal/Gaussian Distribution

1.13.1 Introduction to gaussian or Normal distribution

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1.13.2 Application of gaussian distribution

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1.13.3 Characteristics of the gaussian distribution

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1.13.4 Normal distribution as a limiting form of binomial distribution

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1.13.5 Solved Problem 1

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2:58

1.13.6 Solved Problem 2

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5:9

1.13.7 Solved Problem 3

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13:30

1.13.8 Solved Problem 4

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1.13.9 Solved Problem 5

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1.13.10 Exercises

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1.14 Exponential Distribution

1.14.1 Introduction to Exponential Distribution

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1.14.2 Exponential Distribution

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1.14.3 Solved Problem 1

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6:55

1.14.4 Solved Problem 2

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4:46

1.14.5 Solved Problem 3

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5:54

1.14.6 Memoryless Property of the exponential distribution

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1.14.7 Solved Problem 4

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1.14.8 Solved Problem 5

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1.14.9 Exercises

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Unit - II : Two - Dimensional Random Variables

105 Learning Materials

2.1 Two Dimensional Random Variables

2.1.1 Introduction

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2.1.2 Joint Probability Distribution

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2.1.3 Joint Cumulative Distribution Function

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2.1.4 Marginal Probability Distribution Function

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2.1.5 Conditional Probability Distribution Function

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2.1.6 Expectation of a Function g(X, Y)

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2.2 Problems based on Discrete Random Variables

2.2.1 Introduction

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2.2.2 Solved Problem 1

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10:35

2.2.3 Solved Problem 2

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10:14

2.2.4 Solved Problem 3

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10:56

2.2.5 Solved Problem 4

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2.2.6 Solved Problem 5

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2.2.7 Solved Problem 6

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2.2.8 Solved Problem 7

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2.2.9 Exercises

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2.3 Problems based on Continuous Random Variables

2.3.1 Introduction

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2.3.2 Solved Problem 1

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6:51

2.3.3 Solved Problem 2

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8:28

2.3.4 Solved Problem 3

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8:33

2.3.5 Solved Problem 4

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2.3.6 Solved Problem 5

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2.3.7 Solved Problem 6

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2.3.8 Solved Problem 7

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2.3.9 Solved Problem 8

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2.3.10 Solved Problem 9

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2.3.11 Solved Problem 10

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2.3.12 Solved Problem 11

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2.3.13 Exercises

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2.4 Correlation

2.4.1 Covariance

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2.4.2 Correlation

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2.4.3 Types of Correlation

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2.4.4 Methods of studying correlation

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2.4.5 Scatter Diagram & Simple Graph Method

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2.4.6 Karl Pearson's Coefficient of Correlation

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2.4.7 Properties of Correlation Coefficient

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2.4.8 Solved problem 1

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6:18

2.4.9 Solved problem 2

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8:29

2.4.10 Solved problem 3

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8:26

2.4.11 Solved problem 4

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9:9

2.4.12 Solved problem 5

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2.4.13 Solved problem 6

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2.4.14 Solved problem 7

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2.4.15 Solved problem 8

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2.4.16 Solved problem 9

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2.4.17 Solved problem 10

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2.4.18 Solved problem 11

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2.4.19 Solved problem 12

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2.4.20 Solved problem 13

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2.4.21 Solved problem 14

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2.4.22 Solved problem 15

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2.4.23 Solved problem 16

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2.4.24 Solved problem 17

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2.4.25 Exercises

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2.5 Correlation and Grouped data

2.5.1 Correlation of Grouped Data

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2.5.2 Solved problem 1

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15:7

2.5.3 Solved problem 2

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12:46

2.5.4 Solved problem 3

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2.5.5 Exercises

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2.6 Rank Correlation Coefficient

2.6.1 Rank Correlation Coefficient

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2.6.2 Solved problem 1

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3:42

2.6.3 Solved problem 2

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9:6

2.6.4 Solved problem 3

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2.6.5 Solved problem 4

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2.6.6 Solved problem 5

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2.6.7 Equal or Repeated Ranks

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2.6.8 Solved problem 1

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9:37

2.6.9 Solved problem 2

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2.6.10 Exercises

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2.7 Regression

2.7.1 Introduction

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2.7.2 Methods of studying Regression

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2.7.3 Regression Lines

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2.7.4 Solved problem 1

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9:45

2.7.5 Solved problem 2

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15:28

2.7.6 Solved problem 3

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7:3

2.7.7 Solved problem 4

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2.7.8 Solved problem 5

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2.7.9 Solved problem 6

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2.7.10 Solved problem 7

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2.7.11 Angle Between Two Regression Lines

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2.7.12 Solved problem 1

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4:12

2.7.13 Solved problem 2

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2.7.14 Solved problem 3

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2.7.15 Exercises

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2.8 Transformation of Random Variables

2.8.1 Transformation of Random Variables

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2.8.2 Solved problem 1

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9:38

2.8.3 Solved problem 2

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10:7

2.8.4 Solved problem 3

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13:50

2.8.5 Solved problem 4

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2.8.6 Solved problem 5

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2.8.7 Solved problem 6

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2.8.8 Exercises

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2.9 Central Limit Theorem

2.9.1 Central Limit Theorem [Lindberg-Levy’s form]

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2.9.2 Convergence

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2.9.3 Normal area Property

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2.9.4 Uses of Central Limit Theorem

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2.9.5 Theorem

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2.9.6 Solved problem 1

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4:39

2.9.7 Solved problem 2

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6:14

2.9.8 Solved problem 3

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2.9.9 Solved problem 4

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2.9.10 Solved problem 5

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2.9.11 Solved problem 6

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2.9.12 Solved problem 7

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2.9.13 Area under the Standard Normal Probability Curve

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2.9.14 Exercises

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Unit - III : Random Process

73 Learning Materials

3.1 Random Processes/Stochastic Processes

3.1.1 Introduction

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3.1.2 Random Process

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3.1.3 Random Variable vs Random Process

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3.1.4 Classification of Random process

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3.1.5 Statistical Averages

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3.1.6 Properties of Random process

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3.1.7 Applications of Random process

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3.1.8 Solved Problem 1

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13:1

3.1.9 Solved Problem 2

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3.2 Strict sense stationary (SSS) Processes

3.2.1 Stationary Random Processes/Strict Sense Stationary(SSS) processes

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3.2.2 Important formulae

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3.2.3 Applications of SSS

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3.2.4 Solved Problem 1

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9:39

3.2.5 Solved Problem 2

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5:31

3.2.6 Solved Problem 3

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11:26

3.2.7 Solved Problem 4

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3.2.8 Solved Problem 5

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3.2.9 Exercises

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3.3 Wide sense Stationary (WSS) processes

3.3.1 Wide Sense Stationary(WSS) processes

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3.3.2 Applications of WSS

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3.3.3 Solved Problem 1

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9:24

3.3.4 Solved Problem 2

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9:50

3.3.5 Solved Problem 3

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7:31

3.3.6 Solved Problem 4

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8:51

3.3.7 Solved Problem 5

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3.3.8 Solved Problem 6

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3.3.9 Solved Problem 7

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3.3.10 Solved Problem 8

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3.3.11 Exercises

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3.4 Ergodic Processes

3.4.1 Ergodic Theorem

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3.4.2 Ergodic processes

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3.4.3 Solved Problem 1

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13:22

3.4.4 Solved Problem 2

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5:1

3.4.5 Solved Problem 3

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8:38

3.4.6 Solved Problem 4

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11:35

3.4.7 Solved Problem 5

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3.4.8 Exercises

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3.5 Markov Processes

3.5.1 Introduction to Markov Process

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3.5.2 One step transition probability

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3.5.3 Transition probability matrix

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3.5.4 Probability distribution of a Markov chain

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3.5.5 Chapman – Kolmogorov Theorem

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3.5.6 Stationary distribution for a Markov chain

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3.5.7 Solved Problem 1

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4:56

3.5.8 Solved Problem 2

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15:24

3.5.9 Solved Problem 3

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9:26

3.5.10 Solved Problem 4

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3.5.11 Solved Problem 5

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11:35

3.5.12 Solved Problem 6

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3.5.13 Solved Problem 7

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3.5.14 Solved Problem 8

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3.5.15 Solved Problem 9

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3.5.16 Solved Problem 10

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3.5.17 Exercises

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3.6 Poisson Process

3.6.1 Introduction

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3.6.2 Poisson Process

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3.6.3 Probability function of Poisson process X(t)

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3.6.4 Mean and variance of Poisson Process

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3.6.5 Autocorrelation of Poisson Random Process

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3.6.6 Covariance and Coefficient of correlation of Poisson Process

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3.6.7 Properties of Poisson Process - Property 1 & 2

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3.6.8 Property 3 & 4

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3.6.9 Property 5

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3.6.10 Solved Problem 1

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3:30

3.6.11 Solved Problem 2

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4:41

3.6.12 Solved Problem 3

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9:15

3.6.13 Solved Problem 4

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3.6.14 Solved Problem 5

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3.6.15 Solved Problem 6

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3.6.16 Solved Problem 7

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5:43

3.6.17 Solved Problem 8

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3.6.18 Solved Problem 9

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6:31

3.6.19 Exercises

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Unit - IV : Vector spaces

101 Learning Materials

4.1 Vector Spaces

4.1.1 Introduction

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4.1.2 Theorem 1

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4.1.3 Theorem 2

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4.1.4 Theorem 3

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4.1.5 Theorem 4

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4.1.6 Solved problem 1

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15:27

4.1.7 Solved problem 2

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14:58

4.1.8 Solved problem 3

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11:32

4.1.9 Solved Problem 4

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4.1.10 Solved Problem 5

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4.1.11 Solved Problem 6

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4.1.12 Solved Problem 7

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4.1.13 Solved Problem 8

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4.1.14 Solved Problem 9

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4.1.15 Solved Problem 10

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4.1.16 Solved Problem 11

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4.1.17 Exercises

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4.2 Sub Spaces

4.2.1 Introduction

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4.2.2 Theorem 1

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4.2.3 Theorem 2

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4.2.4 Theorem 3

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4.2.5 Theorem 4

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4.2.6 Theorem 5

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4.2.7 Theorem 6

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4.2.8 Solved problem 1

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3:41

4.2.9 Solved problem 2

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4:27

4.2.10 Solved problem 3

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4:37

4.2.11 Solved Problem 4

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4.2.12 Solved Problem 5

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4.2.13 Solved Problem 6

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4.2.14 Solved Problem 7

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4.2.15 Solved Problem 8

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4.2.16 Solved Problem 9

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4.2.17 Solved Problem 10

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4.2.18 Solved Problem 11

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4.2.19 Exercises

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4.3 Linear Combination and Systems of Equations

4.3.1 Introduction

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4.3.2 Linear Span

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4.3.3 Theorem 1

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4.3.4 Theorem 2

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4.3.5 Theorem 3

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4.3.6 Theorem 4

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4.3.7 Theorem 5

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4.3.8 Theorem 6

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4.3.9 Theorem 7

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4.3.10 Solved problem 1

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3:58

4.3.11 Solved problem 2

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6:3

4.3.12 Solved problem 3

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5:55

4.3.13 Solved Problem 4

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4.3.14 Solved Problem 5

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4.3.15 Solved Problem 6

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4.3.16 Solved Problem 7

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4.3.17 Solved Problem 8

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4.3.18 Solved Problem 9

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4.3.19 Solved Problem 10

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4.3.20 Exercises

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4.4 Linear Dependence and Linear Independence

4.4.1 Introduction

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4.4.2 Theorem 1

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4.4.3 Theorem 2

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4.4.4 Theorem 3

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4.4.5 Solved problem 1

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5:56

4.4.6 Solved problem 2

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5:39

4.4.7 Solved problem 3

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6:7

4.4.8 Solved Problem 4

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4.4.9 Solved Problem 5

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4.4.10 Solved Problem 6

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4.4.11 Solved Problem 7

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4.4.12 Solved Problem 8

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4.4.13 Solved Problem 9

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4.4.14 Solved Problem 10

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4.4.15 Solved Problem 11

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4.4.16 Solved Problem 12

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4.4.17 Exercises

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4.5 Bases

4.5.1 Introduction

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4.5.2 Theorem 1

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4.5.3 Theorem 2

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4.5.4 Theorem 3

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4.5.5 Theorem 4

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4.5.6 Solved problem 1

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6:2

4.5.7 Solved problem 2

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5:26

4.5.8 Solved Problem 3

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4.5.9 Solved Problem 4

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4.5.10 Solved Problem 5

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4.5.11 Solved Problem 6

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4.5.12 Exercises

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4.6 Dimensions

4.6.1 Introduction

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4.6.2 Theorem 1

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4.6.3 Theorem 2

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4.6.4 Theorem 3

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4.6.5 Solved problem 1

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6:25

4.6.6 Solved problem 2

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6:1

4.6.7 Solved problem 3

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5:52

4.6.8 Solved Problem 4

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4.6.9 Solved Problem 5

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4.6.10 Solved Problem 6

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4.6.11 Solved Problem 7

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4.6.12 Solved Problem 8

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4.6.13 Solved Problem 9

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4.6.14 Solved Problem 10

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4.6.15 Solved Problem 11

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4.6.16 Exercises

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Unit - V : Linear Transformation and Inner Product Spaces (Upcoming)

82 Learning Materials

5.1 Linear Transformations

5.1.1 Introduction

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5.1.2 Solved Problem 1

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8:2

5.1.3 Solved Problem 2

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6:2

5.1.4 Solved Problem 3

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5.1.5 Solved Problem 4

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5.1.6 Solved Problem 5

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5.1.7 Solved Problem 6

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5.1.8 Solved Problem 7

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5.1.9 Exercises

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5.2 Algebra of Transformation

5.2.1 Introduction

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5.2.2 Theorem 1

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5.2.3 Solved Problem 1

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7:13

5.2.4 Solved Problem 2

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5.2.5 Solved Problem 3

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7:31

5.2.6 Solved Problem 4

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5.2.7 Solved Problem 5

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5.2.8 Solved Problem 6

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5.2.9 Solved Problem 7

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5.2.10 Exercises

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5.3 Rank and Nullity of a Linear Operator

5.3.1 Introduction

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5.3.2 Theorem

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5.3.3 Solved Problem 1

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6:4

5.3.4 Solved Problem 2

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5.3.5 Solved Problem 3

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7:44

5.3.6 Exercises

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5.4 Rank and Nullity Theorem (Dimension Theorem)

5.4.1 Theorem 1

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5.4.2 Theorem 2

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5.4.3 Theorem 3

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5.4.4 Solved Problem 1

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7:27

5.4.5 Solved Problem 2

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4:31

5.4.6 Solved problem 3

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5.4.7 Solved problem 4

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5.5 Inner Product Space

5.5.1 Introduction

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5.5.2 Solved problem 1

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5.5.3 Solved problem 2

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5.5.4 Solved problem 3

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5.5.5 Solved Problem 4

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5.5.6 Solved Problem 5

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5.5.7 Exercises

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5.6 Norm

5.6.1 Introduction

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5.6.2 Property 1

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5.6.3 Property 2

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5.6.4 Property 3

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5.6.5 Property 4

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5.6.6 Property 5

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5.6.7 Property 6

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5.6.8 Solved Problem 1

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5.6.9 Solved Problem 2

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5.6.10 Solved Problem 3

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5.6.11 Solved Problem 4

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5.6.12 Solved Problem 5

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5.6.13 Solved Problem 6

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5.6.14 Solved Problem 7

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5.6.15 Exercises

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5.7 Orthogonality

5.7.1 Introduction

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5.7.2 Orthonormal

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5.7.3 Theorem 1

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5.7.4 Solved Problem 1

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5.7.5 Solved Problem 2

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5.7.6 Solved Problem 3

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5.7.7 Solved Problem 4

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5.8 Gram Schmidt Orthogonalization

5.8.1 Theorem Gram Schmidt Orthogonalization

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5.8.2 Orthogonal Complement

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5.8.3 Projection Theorem

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5.8.4 Solved Problem 1

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5.8.5 Solved Problem 2

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5.8.6 Solved Problem 3

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5.8.7 Solved Problem 4

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5.8.8 Solved Problem 5

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5.8.9 Exercises

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5.9 Adjoint of Linear Operator

5.9.1 Adjoint of Linear Operator

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5.9.2 Theorems

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5.9.3 Solved Problem 1

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5.9.4 Solved Problem 2

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5.10 Least Squares Approximation

5.10.1 Least Squares Approximation

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5.10.2 Theorems

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5.10.3 Solved Problem 1

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5.10.4 Solved Problem 2

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5.10.5 Solved Problem 3

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5.10.6 Solved Problem 4

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5.10.7 Solved Problem 5

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5.10.8 Exercises

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Important Q&A (MA3355)

75 Learning Materials

1. Probability and Random Variables

1.1 Part A: Q&A

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1.2 Part B: Q&A - 1

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1.3 Part B: Q&A - 2

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1.4 Part B: Q&A - 3

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1.5 Part B: Q&A - 4

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1.6 Part B: Q&A - 5

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1.7 Part B: Q&A - 6

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1.8 Part B: Q&A - 7

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1.9 Part B: Q&A - 8

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1.10 Part B: Q&A - 9

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1.11 Part B: Q&A - 10

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1.12 Part B: Q&A - 11

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1.13 Part B: Q&A - 12

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1.14 Part B: Q&A - 13

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1.15 Part B: Q&A - 14

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1.16 Part B: Q&A - 15

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1.17 Part B: Q&A - 16

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1.18 Part B: Q&A - 17

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1.19 Part B: Q&A - 18

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2. Two - Dimensional Random Variables

2.1 Part A: Q&A

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2.2 Part B: Q&A - 1

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2.3 Part B: Q&A - 2

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2.4 Part B: Q&A - 3

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2.5 Part B: Q&A - 4

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2.6 Part B: Q&A - 5

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2.7 Part B: Q&A - 6

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2.8 Part B: Q&A - 7

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2.9 Part B: Q&A - 8

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2.10 Part B: Q&A - 9

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2.11 Part B: Q&A - 10

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2.12 Part B: Q&A - 11

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2.13 Part B: Q&A - 12

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2.14 Part B: Q&A - 13

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2.15 Part B: Q&A - 14

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2.16 Part B: Q&A - 15

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3. Random Process

3.1 Part A: Q&A

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3.2 Part B: Q&A - 1

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3.3 Part B: Q&A - 2

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3.4 Part B: Q&A - 3

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3.5 Part B: Q&A - 4

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3.6 Part B: Q&A - 5

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3.7 Part B: Q&A - 6

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3.8 Part B: Q&A - 7

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3.9 Part B: Q&A - 8

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3.10 Part B: Q&A - 9

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3.11 Part B: Q&A - 10

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3.12 Part B: Q&A - 11

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3.13 Part B: Q&A - 12

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3.14 Part B: Q&A - 13

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3.15 Part B: Q&A - 14

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3.16 Part B: Q&A - 15

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3.17 Part B: Q&A - 16

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4. Vector spaces

4.1 Part A: Q&A

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4.2 Part B: Q&A - 1

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4.3 Part B: Q&A - 2

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4.4 Part B: Q&A - 3

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4.5 Part B: Q&A - 4

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4.6 Part B: Q&A - 5

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4.7 Part B: Q&A - 6

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4.8 Part B: Q&A - 7

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4.9 Part B: Q&A - 8

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4.10 Part B: Q&A - 9

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4.11 Part B: Q&A - 10

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4.12 Part B: Q&A - 11

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5. Linear Transformation and Inner Product Spaces

5.1 Part A: (Q&A)

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5.2 Part B: Q&A - 1

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5.3 Part B: Q&A - 2

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5.4 Part B: Q&A - 3

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5.5 Part B: Q&A - 4

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5.6 Part B: Q&A - 5

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5.7 Part B: Q&A - 6

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5.8 Part B: Q&A - 7

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5.9 Part B: Q&A - 8

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5.10 Part B: Q&A - 9

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5.11 Part B: Q&A - 10

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Course Instructor

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Promath

787 Courses   •   165783 Students