**Statistics Foundations: Understanding Probability and Distributions**

English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 4h 24m | 509 MB

We live in a world of big data, and someone needs to make sense of all this data. In this course, you will learn to efficiently analyze data, formulate hypotheses, and generally reason about what the ocean of data out there is telling you.

We live in a world of big data: huge amounts of data generated by social networks, governments, consumers and markets. Someone needs to make sense of all this data. In this course, Statistics Foundations: Understanding Probability and Distributions, you will learn the fundamental topics essential for understanding probability and statistics. First, you will have an introduction to set theory, a non-rigorous introduction to probability, an overview of key terms and concepts of statistical research. Then, you will discover different statistical distributions, discrete and continuous random variables, probability density functions, and moment generating functions. Finally, you will use key distribution measures such as mean and variance, and explore topics of covariance and correlation. By the end of this course, you’ll be able to look at data and reason about it in terms of its descriptive statistics and possible distributions.

**Table of Contents**

**Course Overview**

1 Course Overview

**Introducing the Concept of Probability**

2 Course Introduction

3 Module Overview

4 Introducing Sets

5 Set Membership, Null Set, Subsets

6 Set Operations Union, Intersect, Difference

7 Cardinality and Set Complement

8 Some Set Laws

9 Experiments and Events

10 Sample Spaces and Points

11 Set Operations on Events

12 Independence of Events

13 Demo Set Operations

14 Introduction to Probability

15 Rules of Probability

16 Probability Examples

17 Demo Basic Probability

18 Discrete and Continuous Probability

19 Counting Sample Points

20 Multiplication Rule

21 Permutations

22 Permutation Examples

23 Demo Birthday Problem

24 Combinatorial Methods

25 Binomial Coefficients

26 Multinomial Coefficients

27 Probability of a Union of Events

28 Summary

**Calculating the Conditional Probability of Events**

29 Overview

30 Conditional Probability

31 Independence of Events

32 Multiplicative and Additive Laws

33 Law of Total Probability

34 Bayes Theorem

35 Gamblers Ruin Problem

36 Gamblers Ruin Solution

37 Gamblers Ruin Simulation

38 Summary

**Understanding Random Variables and Distributions**

39 Overview

40 Random Variables

41 Discrete Random Variables

42 Discrete Uniform Distribution

43 Binomial Distribution

44 Geometric Distribution

45 Hypergeometric Distribution

46 Continuous Distributions

47 Continuous Uniform Distribution

48 Normal Distribution

49 Gamma Distribution

50 Beta Distribution

51 Summary

**Introducing the Concept of Expectation**

52 Overview

53 Expectation

54 Mean

55 Expectation for a Continuous Distribution

56 Functions of a Random Variable

57 Law of the Unconscious Statistician

58 Properties of Distributions

59 Variance

60 Moments and the Moment Generating Function

61 Means and Variance of Some Distributions

62 Demo Mean and Variance

63 Joint Distributions

64 Probability Mass Function

65 Functions of 2 or More Random Variables

66 Marginal PDFs

67 Covariance and Correlation

68 Demo Covariance and Correlation

69 Summary

**Looking at Some Special Statistical Distributions**

70 Overview

71 Bernoulli Distribution

72 Bernoulli Trials

73 Poisson Distribution

74 Demo Poisson Distribution

75 Normal Distribution Revisited

76 Lognormal Distribution

77 Multinomial Distribution

78 Summary

79 Course Summary

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