Question

If µ and σ² are the mean and variance of the discrete random variable X, and E (X + 3) = 10 and E(X + 3)² = 116, find µ and σ².

Answer 1

Mean = µ, Variance = σ²

Given 

Variance Var (X) = E (X²) — [E(X)]² 

65 – 49 = 16 = σ² 

∴ µ = 7 and σ² = 16