- #1
mrkb80
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Homework Statement
Let [itex] X_1,...,X_n [/itex] be a random sample from a poisson distribution with mean [itex]\lambda[/itex]
Find the MLE of [itex]\lambda^2 + 1 [/itex]
Homework Equations
The Attempt at a Solution
I found [itex]\hat{\lambda}=\bar{x}[/itex]
Can I just square it and add 1 and solve for lambda hat?
If not I have no idea how I would get the FOC (with respect to [itex] \lambda^2 + 1 [/itex])
of the log-likelihood function [itex] \ln{L(\lambda^2+1)}=-n\lambda + \Sigma_{i=1}^n x_i \ln{\lambda} - \ln{\Pi_{i=1}^n x_i!} [/itex]