Suppose that X is a discrete random variable with P(X = 1)
Chapter , Problem 5(choose chapter or problem)
Suppose that X is a discrete random variable with \(P(X=1)=\theta \text { and } P(X=2)=1-\theta\). Three independent observations of X are made: \(x_{1}=1, x_{2}=2, x_{3}=2\)
a. Find the method of moments estimate of \(\theta\).
b. What is the likelihood function?
c. What is the maximum likelihood estimate of \(\theta\)?
d. If \(\Theta\) has a prior distribution that is uniform on [0, 1], what is its posterior density?
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