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
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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
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,
First moment for sample is,
By comparing the first moments of population and sample is, .
Consider,
Hence, the moment estimator is not a biased estimator.
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