# Question: let x and y be random variables the conditional...

###### Question details

. Let X and Y be random variables. The conditional
variance of Y given X, denoted Var(Y | X),

is defined as

Var(Y | X) = E[Y

2

| X] − E[Y | X]

2

.

Show that Var(Y ) = E[Var(Y | X)] + Var(E[Y | X]). (This equality
you are showing is known

as the Law of Total Variance). Hint: From the Law of Total
Expectation, you get Var(Y ) =

E[Y

2

] − E[Y ]

2 = E

h

E[Y

2

| X]

i

− E

h

E[Y | X]

i2

.