Let random variable x represent the number of heads when a f

Let random variable x represent the number of heads when a fair coin is tossed three times. Show all work. Just the answer, without supporting work, will receive no credit.

(a) Construct a table describing the probability distribution.

(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places)

Solution

a) when a fair coin is tossed three times all possible outcomes are, HHH , HHT , HTH , HTT, THH , THT , TTH , TTT

So, x can take values 0,1,2,3.

P(x=0) = 1/8

P(x=1) = 3/8

P(x=2) = 3/8

P(x=3) = 1/8

b) Mean, E(X) = 0 * 1/8 + 1 * 3/8 + 2 * 3/8 + 3 * 1/8

                       = 1.5

E(X²) = 0² * 1/8 + 1² * 3/8 + 2² * 3/8 + 3² * 1/8

          = 3

Var(X) = E(X²) - (E(X))² = 3 - 1.5²

                                      = 0.75

std dev = sqrt(0.75) = 0.866