5. 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 c'. That is, show that E(cX) = cE(X) and V(cX) = c°V(X).
5. 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 c'. That is, show that E(cX) = cE(X) and V(cX) = c°V(X).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![5. 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
c. That is, show that E(cX) = cE(X) and V(cX) = c³V(X).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49589a3c-78d6-4038-9dc3-bad95649c3b6%2F27348a02-cad1-490c-ae1f-0f9c4df8650a%2Filyb11a_processed.png&w=3840&q=75)
Transcribed Image Text:5. 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
c. That is, show that E(cX) = cE(X) and V(cX) = c³V(X).
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