Let T and S be two independent exponential random variables. Let ? be the rate of T and µ the rate of S.(a) What is the distribution of the ?rst order statistic, i.e. random variable min(T,S)?(b) Calculate the probability of T < S.

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Let T and S be two independent exponential random variables. Let ? be the rate of T and µ the rate of S.(a) What is the distribution of the ?rst order statistic, i.e. random variable min(T,S)?(b) Calculate the probability of T < S.