(a) Y1, Y2, ..., Yn form a random sample from a probability distribution with cumu- lative distribution function Fy(y) and probability density function fy(y). Let Y(1) = min{Y1, Y2,..., Yn}. Write the cumulative distribution function for Y(1) in terms of Fy(y) and hence show that the probability density function for Y(1) is fy, (y) = n{1– Fy(y)}"-'fy(y).
(a) Y1, Y2, ..., Yn form a random sample from a probability distribution with cumu- lative distribution function Fy(y) and probability density function fy(y). Let Y(1) = min{Y1, Y2,..., Yn}. Write the cumulative distribution function for Y(1) in terms of Fy(y) and hence show that the probability density function for Y(1) is fy, (y) = n{1– Fy(y)}"-'fy(y).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 52CR
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