Module 6: Probabilistic Reasoning Through the Basic Sampling Model

One mechanism for assisting in various tasks encountered in probabilistic reasoning is to adopt a simple sampling model. A population of interest is first posited, characterized by some random variable, say X . This random variable has a population distribution (often assumed to be normal), characterized by (unknown) parameters. The sampling model posits n independent observations on X , denoted by X1, . . . , Xn, and which constitutes the sample. Various functions of the sample can then be constructed (that is, various statistics can be computed such as the sample mean and sample variance); in turn, statistics have their own sampling distributions. The general problem of statistical inference is to ask what sample statistics tell us about their population counterparts; for example, how can we construct a confidence interval for a population parameter such as the population mean from the sampling distribution for the sample mean. Under the framework of a basic sampling model, a number of topics