Theory Of Point Estimation Solution Manual -

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

$$\frac{\partial \log L}{\partial \lambda} = \sum_{i=1}^{n} \frac{x_i}{\lambda} - n = 0$$ theory of point estimation solution manual

Here are some solutions to common problems in point estimation: Taking the logarithm and differentiating with respect to

Taking the logarithm and differentiating with respect to $\mu$ and $\sigma^2$, we get: theory of point estimation solution manual

Suppose we have a sample of size $n$ from a normal distribution with mean $\mu$ and variance $\sigma^2$. Find the MLE of $\mu$ and $\sigma^2$.

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

Solving these equations, we get: