# Thread: MLEs for a Geometric distribution

1. ## MLEs for a Geometric distribution

Let X1,...Xn be a random sample from a geometric distribution, X~GEO(p). Find the MLEs of the following quantities: (using the invariance property of the MLE)
a) p;
b)E(X) = 1/p^2;
c) Var(X) = (1-p)/p^2;
d) P[X>8] = (1-p)^8.

2. well
what is the MLE of p?

3. ## p?

Is the MLE of p equal to p?

Please explain why.

4. P is an unknown parameter
You need to find a statistics (function of just the X's)
to estimate p.
First obtain the likelihood function and differentiate it wrt p.