Suppose that the random variables X1, , Xk are independent and Xi has the exponential distribution with parameter i (i 1, , k) Let Y min X1, , Xk Show that Y has the exponential distribution with parameter 1 k

Question: Suppose that the random variables X1, . . . , Xk are independent and Xi has the exponential distribution with parameter i (i = 1,

Suppose that the random variables X1, . . . , Xk are independent and Xi has the exponential with parameter βi (i = 1, . . . , k). Let Y = min{X1, . . . , Xk}. Show that Y has the exponential with parameter β1 + . . . + βk.

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