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

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- Nov 19th 2009, 06:44 AMnoob mathematicianfinding expected value
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 - Nov 19th 2009, 09:36 PMmatheagle
- Nov 19th 2009, 11:13 PMnoob mathematician
Suppose now How to find the mle (maximum likelihood estimate) of p, based on the whole sample.

- Nov 19th 2009, 11:20 PMmatheagle
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. - Nov 20th 2009, 12:03 AMnoob mathematician
Given the Y_i defined by u:

Let say now I want to know the MLE of p(1-p), is it right for me to conclude that it is ? - Nov 20th 2009, 12:12 AMmatheagle
I believe that is correct under the invariance principle of MLEs.