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Probability and Statistics

U1
Introduction
topic 1 to 7
7 topics
01
Introduction: Statistics and Data Analysis
02
Statistical Inference
03
Samples, Populations, and the Role of Probability
04
Sampling Procedures
05
Discrete and Continuous Data
06
Statistical Modeling
07
Types of Statistical Studies
U2
Probability
topic 8 to 14
7 topics
08
Probability: Sample Space, Events, Counting Sample Points
09
Probability of an Event
10
Additive Rules
11
Conditional Probability
12
Independence and the Product Rule
13
Bayes’ Rule
14
Random Variables and Probability Distributions
U3
Mathematical Expectation
topic 15 to 31
17 topics
15
Mathematical Expectation: Mean of a Random Variable
16
Variance and Covariance of Random Variables
17
Means and Variances of Linear Combinations of Random Variables
18
Chebyshev’s Theorem
19
Discrete Probability Distributions
20
Continuous Probability Distributions
21
Fundamental Sampling Distributions
22
Sampling Distributions and Data Descriptions
23
Random Sampling
24
Sampling Distributions
25
Sampling Distribution of Means and the Central Limit Theorem
26
Sampling Distribution of S2
27
t-Distribution
28
F-Quantile and Probability Plots
29
Single Sample & One- and Two-Sample Estimation Problems
30
Single Sample & One- and Two-Sample Tests of Hypotheses
31
The Use of P-Values for Decision Making in Testing Hypotheses
U4
Regression
topic 32 to 36
5 topics
32
Regression: Linear Regression and Correlation
33
Least Squares and the Fitted Model
34
Multiple Linear Regression and Certain Nonlinear Regression Models
35
Linear Regression Model Using Matrices
36
Properties of the Least Squares Estimators

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