Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Given: A die is thrown two times.
When a die is tossed two times then the number of observations will be (6 × 6) = 36.
Now, let X is a random variable which represents the success and is given as six appears on at least one die.
Now
P(X = 0) = P(six does not appear on any of die) 
P(X = 1) = P(six appears atleast once of the die) 
P(X = 2) = P(six does appear on both of die) 
Hence, the required probability distribution is,
X | 0 | 1 | 2 |
P(X) |
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Therefore Expectation of X E(X):
11