Set Notation

Interpretation of set operations

Set theory facts

Probability - some discussion

Probability measures

Random variables

Examples of variables that can be thought of as Random Vars

PMF - Probability Mass Function

Example

PDF - Probability Density Function

Example

CDF and survival function

Example

Quantiles

Example

Expectation

Center of mass for a continuous body

Variance

Example

p <- seq(0, 1, length = 1000)
plot(p, p*(1-p), frame=FALSE, type='l', lwd=3)

Example

Interpretting Variances / Chebyshev inequality

Conditional Probability and Density

Intuition

Definition

Conditional densities & mass functions

prob_week2

Notes

prob_week2

Example

Random Vectors

Independent Events

Example

Useful fact

IID random variables

Example