Question

A coin returns heads with probability 1 3 . You keep flipping the coin until the most recent flips is heads and the two immediately preceding flips were tails (that is you stop flipping the coin until the pattern T,T,H appears). Let Y denote the number of flips made. Compute E[Y ].

Answer 1

Answer:

E(Y) = 1.666667

Step-by-step explanation:

By E(Y), we mean the expected value of Y. This is given as:

E(Y) = $\sum{FY}$,

Where F is the frequency.

As given:

The sample space (S) = {T,T,H}

And has a probability of:

H = 1/3

T = 2/3.

Frequency:

H = 1

T = 2.

Thus,

E(Y) = 1*(1/3) + 2*(2/3)

E(Y) = 1.666667.