Question

if x and y are two independent random variables with E(X) = E(Y) show that E[X(X-Y)] = var (X)​

Answer 1

Answer:

E[X(X-Y)]=Var(X). (A)

As given E(X)=E(Y) (1)

we take L.H.S of above equation

E[X(X-Y)]

=E[X^2-XY]

=E(X^2)-E(XY)

=E(X^2)-E(X)E(Y)

=E(X^2)-E(X)E(X)

=E(X^2)-[E(X)]^2 ( var(x)=E(x^2)-[E(x)]^2)

=Var(X)

Answer 2

abe wo jara jaban sambhal ke baat kar ok

wo jaisi bhi hai teri kya hai ab bada aya bolne wala cute hai chal nikal ab yaha se