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.
$$E(X)=5 $$
$$E(Y)=-3 $$
$$E(Z)=-7 $$
$$Var(X)=49 $$
$$Var(Y)=32 $$
$$Var(Z)= 47 $$
Compute the values of the expressions below.
E(-2Z-4)=
E((5z-3X)/4))=
Var(5Y+2)=
E(-5Z^2)=
I tried to substitute 1.$$E(-2Z-4)= -2(-7)-4=10$$ Is this format correct? Please Help!
$E(-2Z-4)= -2(-7)-4=10$ is right because
$$E(-2Z-4)= E(-2Z) +E(-4)$$
$$-2E(Z) +E(-4)$$
$$-2E(Z) +(-4)$$
$$-2E(Z) -4$$
$$ = -2(-7)-4=10$$
The other two that have only $E$ and not $Var$ are similar. For the $Var$, use the rule that
$$Var(aY+b) = a^2Var(Y)$$