1. The problem statement, all variables and given/known data Suppose X has a Poisson distribution with parameter lambda. Given a random sample of n observations, Find the MLE of lambda, and hat lambda. Find the expected value and variance of hat lambda. Show that hat lambda is a consistent estimator of lambda. 2. Relevant equations PX(x) = e^-lambda.lambda^x/x! E(X) = lambda ??? or mean var (X) = lambda ?? or mean 3. The attempt at a solution I am really struggling with stats, hope someone can help. I try to find likelihood function L(x1,x2,...,xn|lambda) = e^-lambda.lambda^x/x! = capital pi from i=1 to n, e^-lambda.lambda^xi/xi! then I'm stuck. Differentiating with respect to lambda, -e^-lambda.xlambda^(x-1)/x! is that the answer??? sorry about the notation also, is there somewhere on this site to get the symbols? Any help greatly appreciated.