0. Define the mean value of a discrete random variable and the probability gener
ID: 3052091 • Letter: 0
Question
0. Define the mean value of a discrete random variable and the probability generating function . Show that the mean value is (1). If (s) has the form p(s)/q(s) show that the mean value is (p (1) q (1))/q(1).
Two duellists, A and B, fire at each other in turn until one hits the other. Each duellist has the same probability of obtaining a hit with each shot fired, these probabilities being a for A and b for B. If A fires the first shot, calculate the probability that A wins the duel. Find also the probability distribution of the number of shots fired before the duel terminates. What is the expected number of shots fired? (Oxford 1976)
Explanation / Answer
Probability of A win = a + (1-a)(1-b)a+......
= a/(1-(1-a)(1-b)) = a/(a+b-ab)
Its sum for infininf GP
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