← STAT 02360 · Probability and Random Variables
STAT 02360 · Random variables
Expectation & variance
Definition
E[X]=Σ x p(x) or ∫ x f(x) dx. Linearity: E[aX+bY]=aE[X]+bE[Y] always. Var(X)=E[(X−μ)²]=E[X²]−μ². SD=√Var.
Read this
Linearity does not require independence. Var(X+Y)=VarX+VarY if uncorrelated/independent.
Indicator variables turn counting problems into easy expectations.
Units: variance is squared units; quote SD when interpreting spread.
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Attempt each problem first, then open the worked solution.
1.For X with P(X=1)=P(X=3)=1/2, find E[X] and Var(X).