How do you find the maximum likelihood estimate of this function?
$$P_x(k;\theta) = \frac{\theta^{2k} e^{-\theta^2}}{k!}$$
I'm really just having trouble with the factorial part... really not sure how to approach this problem.
Thanks
2026-03-30 02:50:38.1774839038
Maximum Likelihood Estimate With Factorial
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The likelihood function you're maximizing is a function of $\theta$ so the $k!$ is just a multiplicative constant. It has no effect on what value of $\theta$ maximizes the function. (One way to see this is that it will clear when you take the derivative and set it to zero.)