HW3a - If X is exponential with parameter , show that the...

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If X is exponential with parameter λ , show that the ‘ceiling’ of X (i.e., the next integer) Y has geometric distribution with parameter p = 1 - exp( - λ ) . Hint: Consider P ( Y = 1) = P (0 < X < 1) , generalize for any i , and compare with the pmf of the geometric which is P ( Y = i ) = p (1 - p ) i - 1 . If X 1 ,...,X n are exponentially distributed, show that the distribution of Y = min( X 1 ,...,X n ) is exponential with parameter
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This note was uploaded on 01/16/2011 for the course STAT 213 taught by Professor Ioannam during the Fall '09 term at Duke.

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