Proof that expected value of constant times X = constant times expected value of X: E(aX) = aE(X)

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Proof that variance of a constant times X is the constant squared times var of X: Var(aX)=a^2 Var(X)

Examples finding expected value of a constant: E(a) = a, and expected value of X: E(X)

Expectation of a constant times a random variable

Expectation of a constant times a function of a random variable

Expected Value of a Constant times a Random Variable

For any constant a and b, E[aX+b]=aE[X]+b and E[aX-b]=aE[X]-b (Discrete)

Properties of Expected Value: aE(X)+b = E(aX + b)

Variance