Solution :
a).
Now, if X = Y, then :
Then, E[X|Y] = x = y
So,
= 0
Therefore, this statement is TRUE.
b). If X = Y , then Var (X) = Var (Y)
And as Var (X|Y) = 0, so Var (X|Y) ≠ Var (X), except when all the elements of Y are same.
So this statement is FALSE.
c). As defined earlier,
So, this statement is also TRUE.
d). The statement is TRUE because .
e). FALSE
Because,