3.4, 3.5 - Random Variables,

Random Variable (X): A single numerical value based on a random event

1. Discrete Random Variables, Integers

2. Continuous Random Variables

Disjoint Events

Expectation Formula

\mu=E\left(X\right)=\sum X\cdot P\left(X\right)

Variability

\sigma^2=\sum\left\lbrack X^2P\left(X\right)\right\rbrack-\mu^2

Fair Game: Defined as a game that costs as much as its expected payout, so expected profit is 0, a zero-sum game

Gambler’s Fallacy: The mistaken belief that if something happens more frequently than normal during some period, then it will happen less frequently in the future

Area = Proportion = Probability = %

Continuous probabilities are estimated as “the area greater than, less than, or between values”

P (A|B)

A = Event of Interest

| = Given

B = Condition Event