Theory Of Point Estimation Solution Manual -

$$\frac{\partial \log L}{\partial \lambda} = \sum_{i=1}^{n} \frac{x_i}{\lambda} - n = 0$$

The likelihood function is given by:

Here are some solutions to common problems in point estimation: theory of point estimation solution manual

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

The likelihood function is given by:

Taking the logarithm and differentiating with respect to $\lambda$, we get:

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

$$\hat{\mu} = \bar{x}$$