As for Property 3 of the exponential distribution, let T1, T2, . . . , Tn be independent exponential random variables with parameters 1, 2, . . . , n, respectively, and let U min{T1, T2, . . . , Tn}. Show that the probability that a particular random variable Tj will turn out to be smallest of the n random variables is P{Tj U}

j n

i1 i, for j 1, 2, . . . , n.

(Hint: P{Tj U} 

0 P{Ti Tj for all i  jTj t}

je

j t

dt.)