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.

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- Mar 11th 2011, 10:44 PMcangerMLEs 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. - Mar 11th 2011, 10:47 PMmatheagle
well

what is the MLE of p? - Mar 12th 2011, 01:46 AMcangerp?
Is the MLE of p equal to p?

Please explain why. - Mar 12th 2011, 06:58 AMmatheagle
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.