2. A random variable X follows Beta(2,3) distribution.(a) Show that the cumulative distribution function F of a Beta(2,3) random variable isF(x) = 6x?823 + 3x4, r € [0, 1].(b) Find the sampling distribution (pdf) of the median for a random sample of size n =2m +1 from Beta(2,3).

Here, Beta(2,3) F(x) = 6x^2 - 8x^3 + 3x^4

2. A random variable X follows Beta(2,3) distribution. (a) Show that the cumulative distribution function F of a Beta(2,3) random variable is F(x) = 6x? – 82³ + 3x*, r € [0, 1]. (b) Find the sampling distribution (pdf) of the median for a random sample of size n = 2m +1 from Beta(2,3).

2. A random variable X follows Beta(2,3) distribution. (a) Show that the cumulative distribution function F of a Beta(2,3) random variable is F(x) = 6x? – 82³ + 3x*, r € [0, 1]. (b) Find the sampling distribution (pdf) of the median for a random sample of size n = 2m +1 from Beta(2,3).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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Question

2. A random variable X follows Beta(2,3) distribution.
(a) Show that the cumulative distribution function F of a Beta(2,3) random variable is
F(x) = 6x?
823 + 3x4, r € [0, 1].
(b) Find the sampling distribution (pdf) of the median for a random sample of size n =
2m +1 from Beta(2,3).

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