Question

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

Answer 1

Let X denote the success of getting heads.

Therefore, the sample space is

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

It can be seen that X can take the value of 0, 1, 2, or 3.

∴ P (X = 1) = P (HHT) + P (HTH) + P (THH)

∴P(X = 2) = P (HHT) + P (HTH) + P (THH)

Therefore, the required probability distribution is as follows.

X	0	1	2	3
P(X)

Mean of X E(X), µ =