Math Path
STAT 02360 · Probability and Random Variables

STAT 02360 · Random variables

PMF / PDF / CDF

Definition

Discrete: PMF p(x)=P(X=x). Continuous: PDF f with P(a≤X≤b)=∫ₐᵇ f. CDF F(x)=P(X≤x) for both; F is right-continuous, nondecreasing, F(−∞)=0, F(∞)=1.

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For continuous RVs, P(X=a)=0; probabilities live on intervals.

PDF must be ≥0 and integrate to 1. PMF must sum to 1.

Differentiate CDF (where possible) to recover PDF; jump sizes recover discrete masses.

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  1. 1.Given a simple PMF table, find P(X≥2) and sketch the CDF.