Question

Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-5 ECY)4 E(Z)--8 Var (x)-39 Var (Y)-11 Var (z) 37 Compute the values of the expressions below. E(2 -2z) 35 30 Var (sz)-5-D

Answer 1

(a)

So,

Answer is:

18

(b)

$=rac{5}{3}E(Y)-rac{5}{3}E(Z)$

So,

Answer is:

6.6667

(c)

So,

Answer is:

920

(d)

$E(4Y^{2})=4E(Y^{2})$ (1)

By Theorem:

Substituting values, we get:

$11=E(Y^{2})-(-4)^{2}=E(Y^{2})-16$

So,

Substituting,(4) becomes:

So,

Answer is:

432