Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.

Explanation

The sample space of the experiment consists of `36` elementary events in the form of ordered pairs `(x_i, y_i)`, where `x_i = 1, 2, 3, 4, 5, 6` and `y_i = 1, 2, 3, 4, 5, 6.`
The random variable `X` i.e. the sum of the numbers on the two dice takes the values `2, 3, 4, 5, 6, 7, 8, 9, 10, 11" or " 12`
Now, let `x` be the sum of numbers on the two dice

`x= 2 ; p(2) =1/36`

`x=3 ; p(3) = 2/36`

`x=4 ; p(4) = 3/36`

`x=5 : p(5) = 4/36`

`x=6 ; p(6) = 5/36`

`x=7 ; p(7) = 6/36`

`x=8 ; p(8) = 5/36`

...