Problem
Two coins are simultaneously tossed until one of them comes up a head and the other a tail. The first coin comes up a head with probability p and the second with probability q. All tosses are assumed independent.
(a) Find the PMF, the expected value, and the variance of the number of tosses.
(b) What is the probability that the last toss of the first coin is a head?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.