Question

Prove that E(X-µ)2 = E(X2) – µ2

Prove that V (aX)=a^2 V(X)

Answer 1

what is E and V?

Answer 2

hey girl

Answer 3

i believe expectancy and variance

Answer 4

oh, sry can't help in this :(

Answer 5

let \(E(X)=\mu\)

then \(E[(X-\mu)^2]=E[X^2-2\mu X+\mu^2]\)

\(=E[X^2]-2\mu E[X]+E[\mu^2]=E[X^2]-2\mu\mu-\mu^2\)

\(=E[X^2]-\mu^2\)

Answer 6

use \(V[X]=E[(X-\mu)^2]\) and the first part to get the second part