Question
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Solution
When a dice is rolled once, probability of obtaining six = 
and probability of obtaining a non-six = 
Now X can take values 0, 1, 2.
P(X = 0) = P(six does not appear a die) = P(non-six on both dice)
P(X = 1) = P(six appear exactly on one die)
= P(six on first die and non-six on the second die)
+ P(six on the second die and non-six on the first die)
P(X = 2) = P(six on both the dice) = 
∴ probability distribution of X is
∴ Expectation of X = mean of the variable X
