Question

Two dice are rolled. If a random variable $X$ is defined as the absolute difference of the two numbers that appear on them, then the mean of $X$ is

• A. 0
• B. $\frac{13}{18}$
• C. $\frac{19}{9}$
• D. $\frac{35}{18}$

Answer 1

Answer: (D)

Two dice are rolled
$X=$ Absolute difference of two number

X	$P/X$	$P_i{X}_i$
0	$6/36$	0
1	$10/36$	$10/6$
2	$8/36$	$16/36$
3	$6/36$	$18/36$
5	$2/36$	$10/36$

$\mu ($ Mean $)=\Sigma P_i{X}_i=\frac{0+10+16+18+16+10}{36}$
$=\frac{70}{36}=\frac{35}{18}$