# Question: Prove that the sequence of sample means of IID random

Prove that the sequence of sample means of IID random variables converges in the MS sense. What conditions are required on the IID random variables for this convergence to occur?

**View Solution:**## Answer to relevant Questions

Let, Xk k = 1, 2, 3… be a sequence of IID Cauchy random variables with and let Sn be the sequence of sample means, (a) Show that also follows a Cauchy distribution. (b) Prove that in this case, the sample mean does not ...Let Xk be a sequence of IID exponential random variables with mean of 1. We wish to compute For some constant y (such that y > 25). (a) Find a bound to the probability using Markov’s inequality. (b) Find a bound to the ...A political polling firm is conducting a poll in order to determine which candidate is likely to win an upcoming election. The polling firm interviews likely voters and asks each whether or not they will vote for the ...Let X be a zero- mean, unit- variance, Gaussian random variable and let Y be a chi- square random variable with n–1 degrees of freedom (see Appendix D, section D. 1.4). If X and Y are independent, find the PDF of One way ...A random process is given by X (t) = A cos (ωt) + B sin (ωt), where A and B are independent zero- mean random variables. (a) Find the mean function, µX (t). (b) Find the autocorrelation function, RX,X (t1, t2). (c) ...Post your question