Paul and n other runners compete in a marathon. Their times are independent continuous
Chapter 9, Problem 41(choose chapter or problem)
Paul and n other runners compete in a marathon. Their times are independent continuous r.v.s with CDF F. (a) For j = 1, 2,...,n, let Aj be the event that anonymous runner j completes the race faster than Paul. Explain whether the events Aj are independent, and whether they are conditionally independent given Pauls time to finish the race. (b) For the rest of this problem, let N be the number of runners who finish faster than Paul. Find E(N). (c) Find the conditional distribution of N, given that Pauls time to finish the marathon is t. (d) Find Var(N). Hint: (1) Let T be Pauls time; condition on T and use Eves law. (2) Or use indicator r.v.s.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer