Suppose we have a sample of size $n$ from a Poisson distribution with parameter $\lambda$. Find the MLE of $\lambda$.
$$L(\mu, \sigma^2) = \prod_{i=1}^{n} \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x_i-\mu)^2}{2\sigma^2}\right)$$ theory of point estimation solution manual
The likelihood function is given by:
Taking the logarithm and differentiating with respect to $\lambda$, we get: Suppose we have a sample of size $n$