Question: 8. Let Xi , i = 1, . . . , n be independent continuous random variables, with Xi having failure rate function ri(t). Let

8. Let Xi , i = 1, . . . , n be independent continuous random variables, with Xi having failure rate function ri(t). Let T be independent of this sequence, and suppose that ni

=1 P{T = i} = 1. Show that the failure rate function r(t) of XT is given by

n r(t)=(t)P(Ti|X > t} i=1

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