Theory Of Point Estimation Solution Manual May 2026

Suppose we have a sample of size $n$ from a Poisson distribution with parameter $\lambda$. Find the MLE of $\lambda$.

$$\hat{\sigma}^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i-\bar{x})^2$$ theory of point estimation solution manual

$$L(\lambda) = \prod_{i=1}^{n} \frac{\lambda^{x_i} e^{-\lambda}}{x_i!}$$ Suppose we have a sample of size $n$

The likelihood function is given by:

$$\frac{\partial \log L}{\partial \sigma^2} = -\frac{n}{2\sigma^2} + \sum_{i=1}^{n} \frac{(x_i-\mu)^2}{2\sigma^4} = 0$$ theory of point estimation solution manual