# MLE and sufficient statistic

#### Barioth

##### Member
Hi! I was wondering

In my note we've a Corollary saying:

If T is sufficient for $$\displaystyle \Theta$$, the maximum likelihood estimate is a function of T.

where T is $$\displaystyle T(X_1,X_2,...X_n)$$and X is given by$$\displaystyle f(x|\Theta)$$

I was wondering, isn't every Maximum likelihood estimator a sufficient statistic?

Thanks for passing by!

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