Answered: Help please: Let X1, X2, . . . , Xn be…

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.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 4ECP

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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.

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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