STAT 3201 Lecture Notes - Lecture 18: Random Variable, Independent And Identically Distributed Random Variables

• School: Ohio State University
• Department: Statistics
• Course: STAT 3201
• Professor: Kurtek Sebastian

Document Summary

Let y1, ,yn denote a random sample selected from a population. These random variables are independent and have the same distribution (iid or independent and identically distributed). Used to estimate or make decisions about unknown population parameters. Suppose you have a random sample y1, ,yn. What is a reasonable estimator of : the sample mean. The goodness of this estimate is dictated by the behavior of the random variables. Y1, ,yn and the effect that this behavior has on the estimator. The random variable is therefore an example of a statistic. Definition: a statistic is a function of the observable random variables in a sample and known constants. Because all statistics are functions of the random variables observed in a sample, all statistics are random variables. Thus, all statistics have probability distributions called sampling distributions. The sample mean is a statistic and it varies from sample to sample.