Let X(1),X(2),.....,X(n) be independent and identically distributed random variables each having mean u and standard deviation sigma^2 . Assume that we do not know the distribution of X(i) , n=1......n, Let Y = (X(1)+X(2)+....+X(n) ) / n Prove that the expected value of the random variable Y is u. the variance of the random variable Y is sigma^2 / n What can be said about the distribution of Y when n is large

Let X(1),X(2),.....,X(n) be independent and identically distributed random variables each having mean u and standard deviation sigma^2 . Assume that we do not know the distribution of X(i) , n=1......n, Let Y = (X(1)+X(2)+....+X(n) ) / n Prove that the expected value of the random variable Y is u. the variance of the random variable Y is sigma^2 / n What can be said about the distribution of Y when n is large

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Description: Let X(1),X(2),.....,X(n) be independent and identically distributed random variables each having mean u and standard deviation sigma^2 . Assume that we do not know the distribution of X(i) , n=1......n,Let Y = (X(1)+X(2)+....+X(n) ) / n Prove thatthe

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

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Let Y = (X(1)+X(2)+....+X(n) ) / n

Prove that

the expected value of the random variable Y is u.
the variance of the random variable Y is sigma^2 / n
What can be said about the distribution of Y when n is large

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