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Let Y be a discrete random variable with support on {-1,0, 1} and with probability mass function p(y; 0) := Po(Y = y) depending on the the parameter, such that, with = {01, 02, 03, 04}. The possible values of p(y; 0) are summarized in the following table: (a) (b) y = -1 y = 0 y = 1 0₁ 02 03 04 0.3 0.2 0.1 0.15 0.1 0.4 0.7 0.15 0.6 0.4 0.2 0.7 In case we collect a realization y₁ of Y, find the maximum likelihood estimator of 0. In case we collect two independent realizations y₁ and y2 of Y, find also in this case the maximum likelihood estimator of 0.

Let Y be a discrete random variable with support on {-1,0, 1} and with probability mass function p(y; 0) := Po(Y = y) depending on the the parameter, such that, with = {01, 02, 03, 04}. The possible values of p(y; 0) are summarized in the following table: (a) (b) y = -1 y = 0 y = 1 0₁ 02 03 04 0.3 0.2 0.1 0.15 0.1 0.4 0.7 0.15 0.6 0.4 0.2 0.7 In case we collect a realization y₁ of Y, find the maximum likelihood estimator of 0. In case we collect two independent realizations y₁ and y2 of Y, find also in this case the maximum likelihood estimator of 0.

MATLAB: An Introduction with Applications
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 Y be a discrete random variable with support on {-1,0, 1} and with probability mass function p(y; 0) := Pŋ(Y = y) depending on the the parameter 0, such that 0 € 0, with © = {01, 02, 03, 04}. The possible values of p(y; 0) are summarized in the following table: (b) y = -1 y = 0 y = 1 0₁ 02 03 0.2 0.1 0.3 0.1 0.4 0.7 0.6 0.4 0.2 04 0.15 0.15 0.7 In case we collect a realization y₁ of Y, find the maximum likelihood estimator 0 of 0. In case we collect two independent realizations y₁ and y2 of Y, find also in this case the maximum likelihood estimator of 0.
Transcribed Image Text:Let Y be a discrete random variable with support on {-1,0, 1} and with probability mass function p(y; 0) := Pŋ(Y = y) depending on the the parameter 0, such that 0 € 0, with © = {01, 02, 03, 04}. The possible values of p(y; 0) are summarized in the following table: (b) y = -1 y = 0 y = 1 0₁ 02 03 0.2 0.1 0.3 0.1 0.4 0.7 0.6 0.4 0.2 04 0.15 0.15 0.7 In case we collect a realization y₁ of Y, find the maximum likelihood estimator 0 of 0. In case we collect two independent realizations y₁ and y2 of Y, find also in this case the maximum likelihood estimator of 0.
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