Let X1, ... , Xn be a random sample (i.i.d.) from Geometric(p) distribution with PMFP(X = x) = (1 – p)*p,x = 0, 1, 2, . ..The mean of this distribution is (1 – p)/p.(a):) Find the MLE of p.(b) (s) Find the estimator for p using method of moments.(c)Now let's think like a Bayesian. Consider a Beta prior on p, i.e., p~ Beta(a, B).Find the posterior distribution of p.Hint: For Geometric likelihood, the conjugate prior on p is a Beta distribution.(d)) What is the Bayes estimator of p under squared error loss? Denote it by PB.(e)What happens to på if both a and ß goes to 0?

Let X1,..., X, be a random sample (i.i.d.) from Geometric(p) distribution with PMF P(X = x) = (1 – p)*p, x = 0, 1, 2, .. The mean of this distribution is (1 – p)/p. (a) :) Find the MLE of p. (b) ( s) Find the estimator for p using method of moments. (c) Now let's think like a Bayesian. Consider a Beta prior on p, i.e., p ~ Beta(a, 3). Find the posterior distribution of p. Hint: For Geometric likelihood, the conjugate prior on p is a Beta distribution. (d) What is the Bayes estimator of p under squared error loss? Denote it by PB. (e) What happens to pg if both a and ß goes to 0?

Let X1,..., X, be a random sample (i.i.d.) from Geometric(p) distribution with PMF P(X = x) = (1 – p)*p, x = 0, 1, 2, .. The mean of this distribution is (1 – p)/p. (a) :) Find the MLE of p. (b) ( s) Find the estimator for p using method of moments. (c) Now let's think like a Bayesian. Consider a Beta prior on p, i.e., p ~ Beta(a, 3). Find the posterior distribution of p. Hint: For Geometric likelihood, the conjugate prior on p is a Beta distribution. (d) What is the Bayes estimator of p under squared error loss? Denote it by PB. (e) What happens to pg if both a and ß goes to 0?

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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