(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).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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