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

Given :

The number of possible outcomes when two dice are thrown` =6 times 6=36`


P(X=2)=P(1,1)`=frac{1}{36}`

`P(X=3)=P[(1,2),(2,1)]=frac{2}{36} `

`P(X=4)=P[(1,3),(2,2),(3,1)]=frac{3}{36} `

`P(X=5)=P[(1,4),(2,3),(3,2),(4,1)]=frac{4}{36} `

`P(X=6)=P[(1,5),(2,4),(3,3),(4,2),(5,1)]
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