Let X_1,....,X_n be iid rv with density f and cumulative distribution function F. Let:
I want to find the expected value of
I can't seems to find the answer since the distribution is unknown to me
I would think that these are i.i.d. Bernoulli's.
Let for i=1,2,...,n.
Here isn't really the point
The MLE of Bernoullis is the sample mean of the Y's.
Since the Likelihood function is
Now take the log and differentiate TWICE and obtain the sample mean as the MLE.