Help please: Let X1, X2, . . . , Xn be i.i.d. from a uniform distribution over the interval (0, 1). Let Y = max{X1, X2, . . . , Xn}. Show that the PDF of Y has a Beta distribution. See https://en.wikipedia.org/wiki/Beta_ distribution to find the density of a Beta random variable.

Help please: Let X1, X2, . . . , Xn be i.i.d. from a uniform distribution over the interval (0, 1). Let Y = max{X1, X2, . . . , Xn}. Show that the PDF of Y has a Beta distribution. See https://en.wikipedia.org/wiki/Beta_ distribution to find the density of a Beta random variable.

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

Section13.3: Special Probability Density Functions

Problem 7E

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Question

Help please:

Let X1, X2, . . . , Xn be i.i.d. from a uniform distribution over the interval (0, 1). Let Y = max{X1, X2, . . . , Xn}.
Show that the PDF of Y has a Beta distribution. See https://en.wikipedia.org/wiki/Beta_
distribution to find the density of a Beta random variable.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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