Q. 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
TS EAMCET 2019
Solution:
Two dice are rolled
$X=$ Absolute difference of two number
X
$P/ X$
$P_iX_i$
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 $)=\Sigma P_{i} X_{i}=\frac{0+10+16+18+16+10}{36}$
$=\frac{70}{36}=\frac{35}{18}$
| X | $P/ X$ | $P_iX_i$ |
|---|---|---|
| 0 | $6 / 36$ | 0 |
| 1 | $10/36$ | $10/6$ |
| 2 | $8/36$ | $16/36$ |
| 3 | $6/36$ | $18/36$ |
| 5 | $2/36$ | $ 10/36 $ |