Taking the logarithm and differentiating with respect to $\lambda$, we get:
Solving this equation, we get:
Here are some solutions to common problems in point estimation: theory of point estimation solution manual
$$\hat{\lambda} = \bar{x}$$
In conclusion, the theory of point estimation is a fundamental concept in statistics, which provides methods for constructing estimators that are optimal in some sense. The classical and Bayesian approaches are two main approaches to point estimation. The properties of estimators, such as unbiasedness, consistency, efficiency, and sufficiency, are important considerations in point estimation. Common point estimation methods include the method of moments, maximum likelihood estimation, and least squares estimation. The solution manual provides solutions to some common problems in point estimation. Taking the logarithm and differentiating with respect to
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 $\sigma^2$.
The theory of point estimation is based on the concept of sampling theory. When a sample is drawn from a population, it is rarely identical to the population parameter. Therefore, the sample statistic is used as an estimate of the population parameter. The theory of point estimation provides methods for constructing estimators that are optimal in some sense. Common point estimation methods include the method of
$$\hat{\mu} = \bar{x}$$
$$\frac{\partial \log L}{\partial \sigma^2} = -\frac{n}{2\sigma^2} + \sum_{i=1}^{n} \frac{(x_i-\mu)^2}{2\sigma^4} = 0$$