# Suppose that the failure times are exponential with

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Unformatted text preview: at time t. Suppose that the machines fail at rate i . What is the probability that machine 2 is the ﬁrst to fail? 2.5. Three people are ﬁshing and each catches ﬁsh at rate 2 per hour. How long do we have to wait until everyone has caught at least one ﬁsh? 2.6. Alice and Betty enter a beauty parlor simultaneously, Alice to get a manicure and Betty to get a haircut. Suppose the time for a manicure (haircut) is exponentially distributed with mean 20 (30) minutes. (a) What is the probability Alice gets done ﬁrst? (b) What is the expected amount of time until Alice and Betty are both done? 2.6. EXERCISES 93 2.7. Let S and T be exponentially distributed with rates and µ. Let U = min{S, T } and V = max{S, T }. Find (a) EU . (b) E (V U ), (c) EV . (d) Use the identity V = S + T U to get a di↵erent looking formula for EV and verify the two are equal. 2.8. Let S and T be exponentially distributed with rates and µ. Let U = min{S, T }, V = max{S, T }, and W = V U . Find the variances of U , V , and W. 2.9. In a hardware store you must ﬁrst go to server...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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