Question
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Solution
Clearly, X can take values 0, 1 and 2.
We have
P(X = 0) = Probability of not getting six on any dice =
P(X = 1) = Probability of getting one six =
P(X = 2) = Probability of getting two sixes =
Thus, the probability distribution of X is given by
Computation of mean variance
x_{i} 
p_{i} = P(X = x_{i}) 
p_{i} x_{i} 

0 
25/36 
0 
0 
1 
10/36 
10/36 
10/36 
2 
1/36 
2/36 
4/36 




We have
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