Equate the population moments to the sample moments and solve for the parameters.
: A critical assumption. Two random variables are independent if their joint probability density function (PDF) can be factored into separate parts for each variable. The Factorization Theorem mathematical statistics lecture
Moving beyond single-point guesses, we encounter interval estimation. Rather than providing one value, we provide a range—a confidence interval—that is likely to contain the true parameter. It is a common misconception that a 95% confidence interval means there is a 95% probability the parameter is inside. In frequentist statistics, the parameter is fixed; it is the interval itself that is random. Therefore, the 95% refers to the process: if we repeated the experiment many times, 95% of the calculated intervals would contain the true parameter. Equate the population moments to the sample moments
[ \sqrtn(\hat\theta - \theta) \xrightarrowd N(0, I(\theta)^-1) ] In frequentist statistics, the parameter is fixed; it
