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) |

Therefore Expectation of X E(X):

11