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Let {Xi}ni be IID from Bernoulli(p). Find the method of moments estimator of p and use simulations to check whether your estimator is

Let {Xi}ni be IID from Bernoulli(p). Find the method of moments estimator of p and use simulations to check whether your estimator is

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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 Let {Xi}ni be IID from Bernoulli(p). Find the method of moments estimator of p and use simulations to check whether your estimator is biased or not

Expert Solution
Step 1

From the given information,

X1, X2, ....,Xn are IID random variables with Bernoulli(p).

Consider, the first moment for the population of Binomial distribution is,

E(X)=p

First moment for sample is,

M1=∑Xin      =x¯

By comparing the first moments of population and sample is, p^=x¯.

Consider,

EX¯=EX1+X2+....+Xnn         =1nEX1+EX2+....+EXn        =1np+p+...+p        =p

Hence, the moment estimator is not a biased estimator.

 

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