Try the fastest way to create flashcards
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

Verified
Step 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*}

## Recommended textbook solutions #### A First Course in Probability

8th EditionISBN: 9780136033134 (1 more)Sheldon Ross
1,395 solutions #### Probability and Statistics for Engineers and Scientists

9th EditionISBN: 9780321629111 (4 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers
1,204 solutions #### Probability and Statistics for Engineering and the Sciences

9th EditionISBN: 9781305251809 (9 more)Jay L. Devore
1,589 solutions #### Statistics and Probability with Applications

3rd EditionISBN: 9781464122163Daren S. Starnes, Josh Tabor
2,555 solutions