Ten runners compete in a race starting at time t = 0. The runners' finishing times R1,..., R10 are iid exponential random variables with expected value 1/μ = 10 minutes.
(a) What is the probability that the last runner will finish in less than 20 minutes?
(b) What is the PDF of X1, the finishing time of the winning runner?
(c) Find the PDF of Y = R1 + ... + R10.
(d) Let X1,..., X10 denote the runners' inter-arrival times at the finish line. Find the joint PDF fX1 ...,X10 (x1, ..., x10).