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5주차
1.
Introduction to Probability
and Statistics 5th Week (4/5) 1. Mathematical Expectations 2. Special Probability Distributions
2.
Mathematical Expectations*: Definition -
Discrete - Continuous *in Korean: 기대값
3.
Mathematical Expectations: Example
4.
Mathematical Expectations: Example
5.
Functions of Random
Variables
6.
Functions of Random
Variables
7.
Functions of Random
Variables
8.
A Few Theorems
on Expectation
9.
The Variance and
Standard Deviation
10.
The Variance and
Standard Deviation
11.
The Variance and
Standard Deviation
12.
The Variance and
Standard Deviation
13.
A Few Theorems
on Variance
14.
Compare! Vs. is
true for any random variables is true for only independent variables is true for only independent variables Not “Var(X) – Var(Y)”
15.
Standardized Random Variables
16.
Moments
17.
Moments
18.
Moment Generating Functions
19.
Some Theorems on
Moment Generating Functions
20.
Characteristic Functions
21.
Some Theorems on
Characteristic Functions
22.
Importance of Characteristic
Functions
23.
Variance for Joint
Distributions
24.
Covariance
25.
Some Theorems on
Covariance
26.
Correlation Coefficient
27.
• Correlation coefficient
⇒ 양의 상관관계 ⇒ 음의 상관관계 ⇒ 무 상관관계
28.
Conditional Expectation, Variance,
and Moments
29.
Understanding Conditional Probability
Function When X=x, Conditional When Y=y, Conditional Probability Function for Y Probability Function for X
30.
Chebyshev’s Inequality
31.
Law of Large
Numbers
32.
Other Measures of
Central Tendency
33.
Percentiles
34.
Other Measures of
Dispersion
35.
Skewness
36.
Kurtosis
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