STATS 426 Lecture Notes - Lecture 7: Simple Random Sample, Random Variable, Independent And Identically Distributed Random Variables
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The goal is to estimate the mean and the variance of a variable of interest in a nite population by collecting a random sample from it. Suppose there are n members of the population, numbered 1 through n and let the values assumed by the variable of interest be x1, x2, . In this case the population proportion of voters is the mean of the xi"s. ). We denote the distinct values of the xi"s by. , m and let ni denote the frequency of i in the population. N and the population variance 2 is m. We denote the relative frequencies of the i"s in the population by {p1, p2, . A sample of size n is collected with replacement from the population. Thus, an individual is drawn (randomly), their x value recorded, and the individual is then returned to the population. Now, a second individual is drawn, and the process continues n times.