Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

Answer

N/a

Explanation

Let `X` be a random variable which represents the number of getting 6 on two dice.
Therefore the possible values of `X` are 0,1,or 2.
When a die is thrown the probability of getting `6=1/6`
and probability of not getting `6=5/6`
`P(X=0)=P` (not getting 6 on two dice)
`=5/6xx5/6=25/36`
`P(X=1)=P` (getting 6 on 1st die and not getting 6 on 2nd die) `+P` (not getting 6 on 1st die and getting 6 on 2nd die)
`=1/6xx5/6+1/6xx5/6=5/36+5/36=10/36`
`P(X=2)=P` (getting 6 on two dice)
`=1/6xx1/6=1/36`
Therefore, required probability distribution is

Expectation of `X=` mean of variable `X`
`sumXP(X)=0xx25/36+1xx10/36+2xx1/36`
`=10/36+2/36=12/36=1/3`