Question

A coin is tossed repeatedly until heads has occurred twice or tails has occurred twice, whichever comes first. Let X be the number of times the coin is tossed.

Find: a. E(X). b. Var(X).

The answers are 2.5 and 0.25

Answer 1

Two tails or two heads cannot be obtained in 0 or 1 tosses.

The sample space for tossing of a coin 2 times is : HH,HT,TH,TT out of which 2 heads or 2 tails occur in HH, TT.

The sample space for tossing of a coin 3 times is : HHH,HHT,HTH,THH,HTT,THT,TTH,TTT out of which 2 heads or 2 tails occur in HTH,THH,HTT,THT.

So, Probability distribution of X:

X	2	3
P(X)

a)

b)

Now

So,