As in Example 5.7.3, athletes compete one at a time at the high jump. Let Xj be how high
Chapter 5, Problem 59(choose chapter or problem)
As in Example 5.7.3, athletes compete one at a time at the high jump. Let Xj be how high the jth jumper jumped, with X1, X2,... i.i.d. with a continuous distribution. We say that the jth jumper is best in recent memory if he or she jumps higher than the previous 2 jumpers (for j 3; the first 2 jumpers dont qualify). (a) Find the expected number of best in recent memory jumpers among the 3rd through nth jumpers. (b) Let Aj be the event that the jth jumper is the best in recent memory. Find P(A3 \ A4), P(A3), and P(A4). Are A3 and A4 independent?
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