Answered: 1. Suppose that X1, Xn is an iid random…

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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1. Suppose that X1, Xn is an iid random sample from a distribution with pdf f(x; sigma) = 1/2 * (sigma) * e ^ (- |x| / sigma) - infinity0 0(a) Find the method of moments estimator (MME) of \sigma. Hint: See the example in lecture notes. (b) Find the maximum likelihood estimator (MLE) of \sigma. Hint: See the example in lecture notes. (c) Use central limit theorem to find the large - sample asymptotic distribution of the MLE in part (b). (d) Suppose 10 independent observations were taken from the given distribution: (0.5, 0.8, 2.2, 1.6, 2.0, 2.8, 1.5, 0.9, 2.5, 1.8). What is the numerical value of the MLE? What is the numerical value of the estimated standard deviation (standard error) of the MLE?

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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