1. What would be the MLE of the population proportion p based on a
random sample of size n from the parent b(1,p) if it is known that p is
either 1/2 or 1/4.
I Know that for p= 1/2 the MlE is at x= n/2 in is even or (n-1)/2 and
(n+1)/2 if n is odd. But I don't know for what x the other (when p=3/4)
is max. Coudl u help?
2. Let theta=P9X=0)=exp(-lambda) lambda>0
So the parent dist. is poisson.
I know that exp(-Xbar) is the MLE of theta. But I don't know the
variance of this estimator to show that the variance never reaches the
raro cramer lower bound so that our estimator is not BRUE and not
efficient. In sum, I need to know the variance of the MLE above.
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