Description
A fair quarter is tossed until it comes up heads; suppose X is the number of tosses necessary. If X = x, then x fair pennies are tossed; let Y denote the number of heads on the pennies. Find P(Y = 3), simplifying the result as much as you can.
The coin loaded so as to come up heads 1/3 of the time is tossed until a head appears. This is followed by the toss of a coin loaded so as to come up heads with a probability of 1/4 until that coin comes up heads.
(a) Find the probability distribution of Z, the total number of tosses necessary.
(b) Find the mean and variance of Z.