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Question 1. Let X1,- < 1.Xj be ii.d. Bernoulli random variables with parameter 0,Compute point estimation for 0 based on 1) the method of moments, 2) the maximum...

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Question 1. Let X1,- < 1.Xj be ii.d. Bernoulli random variables with parameter 0,Compute point estimation for 0 based on 1) the method of moments, 2) the maximum likelihood method, 3) the Bayesian method if the prior distribution of A is a Beta distribution whose density is given by 7(0) V(a+B Aa-1 8-1 T(o)r(

Question 1. Let X1,- < 1. Xj be ii.d. Bernoulli random variables with parameter 0, Compute point estimation for 0 based on 1) the method of moments, 2) the maximum likelihood method, 3) the Bayesian method if the prior distribution of A is a Beta distribution whose density is given by 7(0) V(a+B Aa-1 8-1 T(o)r(



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Refer to Exercise $3.86 .$ The maximum likelihood estimator for $p$ is $1 / Y$ (note that $Y$ is the geometric random variable, not a particular value of it). Derive $E(1 / Y) .[\text { Hint: If }|r|<1$, $\left.\sum_{i=1}^{\infty} r^{i} / i=-\ln (1-r) .\right]$.


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