Consider a horse race with 5 horses. The race running time of horse ???? [expressed in minutes] is a random

variable described by ???????? = 2 + ????????, where ???????? follows an exponential distribution with mean value ???????? = 1/i for

i =1,...,5. The horse with the shortest running time wins the race; the race time is the running time of the

winning horse.

a) Compute the expected running time of each horse.

b) Find the expected race time.

c) Find the standard deviation of the race time.

d) Find the probability that the horse considered fastest wins the race.