In Exercise 5.62, we considered two individuals who each tossed a coin until the first
Chapter 5, Problem 5.84(choose chapter or problem)
In Exercise 5.62, we considered two individuals who each tossed a coin until the first head appears. Let Y1 and Y2 denote the number of times that persons A and B toss the coin, respectively. If heads occurs with probability p and tails occurs with probability q = 1 p, it is reasonable to conclude that Y1 and Y2 are independent and that each has a geometric distribution with parameter p. Consider Y1 Y2, the difference in the number of tosses required by the two individuals. a Find E(Y1), E(Y2), and E(Y1 Y2). b Find E(Y 2 1 ), E(Y 2 2 ), and E(Y1Y2) (recall that Y1 and Y2 are independent). c Find E(Y1 Y2)2 and V(Y1 Y2). d Give an interval that will contain Y1 Y2 with probability at least 8/9.
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