please c) and d) parts Question 2Suppose that we have data y = (v₁,...,yn). Each data-point y; is assumed to be generated by adistribution with the following probability density function:>= 1 / XP(-21).«(-9). Viexpp(yi|0) =Yi ≥ 0.The unknown parameter is 0, with 0 > 0.(a) Write down the likelihood for given y. Find an expression for the maximum likelihoodestimate (MLE) Ô.(b) A Gamma(a, 3) distribution is chosen as the prior distribution for 8. Derive the resultingposterior distribution for 8 given y.(c) We would like to choose the gamma prior distribution parameters so that a = 1, andP(0> 50+B) = 0.05,B = 2Find the value of 3 that is needed.(d) The data are y = (4,4,8,8,4, C+3), Gia the last digit of you. In aber, withn = 6.C = 3(i) What is the MLE(ii) Using the prior distribution from part (c), what are the parameters of the posteriordistribution for ?(iii) What are the posterior mean and standard deviation for A?

Given that each data point from the data follows the probability density function:

Answered: Question 2 Suppose that we have data y…

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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