## Related questions with answers

Question

The joint probability mass function of the random variables X, Y, Z is

$p ( 1,2,3 ) = p ( 2,1,1 ) = p ( 2,2,1 ) = p ( 2,3,2 ) = \frac { 1 } { 4 }$

Find (a) E[XYZ], and (b) E[XY+XZ+YZ].

Solution

VerifiedStep 1

1 of 2#### (a)

Observe that the random variable $XYZ$ can assume values $2,4,6,12$ with the same probability $\frac{1}{4}$. Hence, the required expectation is

$\begin{align*} E(XYZ) = \frac{1}{4} (2+4+6+12) = 6 \end{align*}$

#### (b)

Observe that the random variable $XY + XZ + YZ$ can assume values $11,5,8,16$ with the same probability $\frac{1}{4}$. Hence, the required expectation is

$\begin{align*} E(XY+XZ+YZ) = \frac{1}{4} (11+5+8+16) = 10 \end{align*}$

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