Statistics average value question

[kidsasd987]

Homework Statement

Prove that A(X(ω_k)²)≥A(X(ω_k))² if and only if X(ω_k) has the same value for every k such that p_k>0 for every category which actually occurs in the population

Homework Equations

A(X)=1/N∑n_kX(ω_k)=∑p_kX(ω_k)

The Attempt at a Solution

A[(X-A(X)²)]=A(X²)-A(X)²

and i believe the question itself is ill-structured because A(X²)-A(X)² implies A(X²)≥A(X)² for all X(ω_k) since variance cannot be a negative value. Please confirm with me. Thanks

 

[Orodruin]

The intended question is probably missing the statement "... with equality if and only if ..."