STAT 1000Q Study Guide - Final Guide: Central Limit Theorem, Independent And Identically Distributed Random Variables, Variance

• School: UConn
• Department: Statistics
• Course: STAT 1000Q
• Professor: Randolph Ewart

Document Summary

Let x1, x2, x3 be a sequence of independent random variables, each with the same distribution and mean for every e > 0. Consider a sample x1 xn from a general population that has a population of mean ( ). Lln is also used to show that for large sample variance s2 is close to population variance 2. Let x1, x2, x3 be a sequence of independent identically distributed random variables with mean and standard deviation 2 s2 = 2. Clt tells us that when sample size n is large (n>30) then, Sample mean is approximately normally distributed with mean and variance 2 / n or. The sum x1 + xn is also approximately distributed with mean and variance or . Consider a sample x1 xn from a population with mean and variance. Mathematically, we deal with n independently identically distributed random variables. The sample mean is a variable that is given by .