Question

A pair of dice is thrown and X denotes the absolute difference of the numbers on uppermost faces. Then the expected value of X is ______

Options

• `5/18`

• `3/18`

• `35/18`

• `7/18`

Answer 1

A pair of dice is thrown and X denotes the absolute difference of the numbers on uppermost faces. Then the expected value of X is `underline(35/18)`.

Explanation: 

X can take values 0, 1, 2, 3, 4, 5. The probability distribution of X is

X	0	1	2	3	4	5
P(X)	`6/36`	`10/36`	`8/36`	`6/36`	`4/36`	`2/36`

∴ E(X) = `sumx_i.P(x_i)`

= `6/36 xx 0 + 10/36 xx 1 + 8/36 xx 2 + 6/36 xx 3 + 4/36 xx 4 + 2/36 xx 5`

⇒ E(X) = `1/36`(0 + 10 + 16 + 18 + 16 + 10)

⇒ E(X) = `70/36 = 35/18`