Let U1, . . . , Un be a random sample from the Unif(0,1) distribution.(a) Find the distribution of Y1 = −2 log U1 .(b) Show that the distribution Y = −2 ∑ni=1 log Ui is χv2 for some value of ν.(c) What is the value of ν in part (b)?

The objective of the question is to find the distribution of a transformed random variable and to…

Answered: Let U1, . . . , Un be a random sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let U1, . . . , Un be a random sample from the Unif(0,1) distribution. (a) Find the distribution of Y1 = −2 log U1 .(b) Show that the distribution Y = −2 ∑ni=1 log Ui is χv2 for some value of ν. (c) What is the value of ν in part (b)?