Statistics Foundations: Understanding Probability and Distributions

Statistics Foundations: Understanding Probability and Distributions
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