2A discrete random variable Y takes the values -1, 0 and 1 with probabilities 10, 1-0 and 10respectively. Let Y₁ and Y₂ be two independent random variables, each with the samedistribution as Y.(a) List the possible values of {Y1, Y2) that may arise and calculate the probability of each.Verify that your probabilities sum to unity.(b) By calculating the value of (Y₂ - Y₁)² for each possible pair (Y₁, Y2), determine thesampling distribution of (Y₂ - Y₁)²..(c) Show that X = (Y₂Y₁)² is an unbiased estimator for 0, and find Var(X) as a functionof 0.(d) Now suppose that Y₁, Y2..... Y, are n independent observations on the random variableY. Since is the probability that Y is not zero, a possible estimator for 0 is the proportion, Z,of non-zero values among Y₁, Y2,, Y. Write down the mean and variance of Z, andstate, giving your reasons, which of X and Z you would prefer as an estimator for 8 whenn = 2.

Answered: Image /qna-images/answer/8a4814eb-c368-4a81-92fe-cfc251f6b808.jpg

Answered: 2 A discrete random variable Y takes…

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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