Question

Two runners compete in the NYC Marathon. Runner A’s finishing time is uniformly distributed over the interval (125, 130), and Runner B’s finishing time is uniformly distributed over the interval (126, 131). Additionally, suppose the times for Runners A and B are independent random variables. Let Runner A’s time be X_a and Runner B’s time be X_B.

a) What is the probability that Runner B finishes before Runner A?

(b) Compute E[X_A − X_B].

(c) Set-up (BUT DO NOT INTEGRATE) an expression for E[ |X_A − X_B| ], the expectation of the difference in the runner’s times. Your answer should not involve any absolute value signs.

Answer 1