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3-84. Show that for a discrete uniform random variable X , if each of the values in the range of X is multiplied by the constant c, the effect is to multiply the mean of X by c and the variance of X by c². That is, show that E(cX)=cE(X)and V(cx)=c²v(x). %3D

3-84. Show that for a discrete uniform random variable X , if each of the values in the range of X is multiplied by the constant c, the effect is to multiply the mean of X by c and the variance of X by c². That is, show that E(cX)=cE(X)and V(cx)=c²v(x). %3D

A First Course in Probability (10th Edition)
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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3-84. Show that for a discrete uniform random variable X, if each of the values in the range of X is multiplied by the constant c, the effect is to multiply the mean of X by c and the variance of X by c². That is, show that E(cX)=cE(x) and V (cX)=c²v(x).
Transcribed Image Text:3-84. Show that for a discrete uniform random variable X, if each of the values in the range of X is multiplied by the constant c, the effect is to multiply the mean of X by c and the variance of X by c². That is, show that E(cX)=cE(x) and V (cX)=c²v(x).
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