Canonical syllabus units, structured theorems, lecture notes, and past examination problems.
Covers evaluating estimators based on unbiasedness, efficiency, and consistency, including showing sample mean properties for Poisson and binomial distributions
Involves constructing a 99% confidence interval for the mean shaft diameter given sample statistics
Focuses on finding sufficient statistics for parameters in given probability density functions
Covers deriving moment estimators for parameters of a uniform distribution and calculating estimates from sample data
Involves obtaining the maximum likelihood estimator for the parameter of a geometric distribution and computing it for a given sample
Using matrix notation to fit a straight line by the method of least squares
Focuses on finding a Minimum Variance Unbiased Estimator (MVUE) or a Uniformly Minimum Variance Unbiased Estimator (UMVUE). It establishes the necessary and sufficient conditions for an MVUE to exist via likelihood functions, introduces the Schwartz inequality proof, explains Fisher's Information, and details how to find the lower variance limit using the Cramer-Rao Inequality (CRI)
Covers generating narrow confidence intervals (confidence limits) that enclose an unknown parameter with a high probability. Assuming a normal population, it walks through deriving and computing 100(1-alpha)% confidence intervals for the population mean (mu) and variance (sigma squared) under different scenarios: when sigma squared is known or unknown, and when mu is known or unknown
Extends interval estimation to look at two independent populations (X1 and X2). It details how to derive and compute a 100(1-alpha)% confidence interval for the true mean difference (mu1 - mu2) under two primary cases: when the common variance is known or unknown