I have 3 questions;
1. Suppose that X1,...Xn form a random sample from a normal distribution for which both the mean and variance are unknown. Find the MLE of the 0.95 quantile of the distribution, that is, of the point "theta" such that Pr(X < "theta") = 0.95.
2. Suppose that X1,...,Xn form a random sample from an exponential distribution for which the value of the parameter B(beta) is unknown. Determine the M.L.E. of the median of the distribution.
3. Suppose that X1,..,Xn form a random sample from a distribution for which the pdf f(x|theta) is as follows:
f(x|theta) = (theta)(x)^(theta -1)
Also suppose that the value of theta is unknown (theta >0). Find the M.L.E of theta.
I obviously don't have a good grasp on MLE.
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