Let X and Y be independent standard normal random variables. Determine the pdf ofW = x² + y². Find the mean and the variance of U = /W.Let Y₁, Y₂, ..., Yn denote a random sample of size n from a population with a uniform distributionon the interval (0, 0). Consider = Y(1) = min(Y₁, Y₂, ..., Y₁) as an estimator for 0. Show thatis a biased estimator for 0.Let X and Y be independent exponentially distributed random variables with parameterXλ = 1. If U = X + Y and V =. Find and identify the marginal density of U.X+Y

As per bartleby guidelines we can solve only first question and rest can be reposted

Answered: Let X and Y be independent standard…

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 X and Y be independent standard normal random variables. Determine the pdf of W = x² + y². Find the mean and the variance of U = W.