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(Solved): Consider a Binomial random variable xBinomial(n,\theta ), where n is known but \theta is unknown. ...
Consider a Binomial random variable x?Binomial(n,\theta ), where n is known
but \theta is unknown.
Denote hat(\theta )=(x)/(n). Answer the following questions:
(a) (5 points) Show that hat(\theta ) is unbiased for \theta .
(b) (10 points) Given a function g(t)=nt(1-t). Check if g(hat(\theta )) is an unbiased
estimator for g(\theta ). Please justify your answer.
(c) (5 points) Find an unbiased estimator for g(\theta ).