Find the mean number of heads in three tosses of a fair coin.

Explanation

The sample space of given experiment is
S =({(HHH), (HHT), (HTT), (TTT), (TTH), (THH), (HTH), (THT)}
Let X denotes the no. of heads in three tosses of a fair coin
Here, X is random which may have values `0, 1, 2, 3`.
Therefore, Probability distribution is, `P(X = 0) = 1/8,P(X = 1)`
= `3/8 P(X = 2) = 3/8, P(X = 3) = 1/8`
∴ Mean number `(E(x)) = ∑p_ix_i = 0 * 1/8 + 1 *3/8 + 2 * 3/8 + 3 * 1/8`
= `(3 + 6 + 3)/8 = 12/8 = 3/2 = 1.5`