5. Show that for a discrete uniform random variable X, if each of the values in the range of X ismultiplied by the constant c, the effect is to multiply the mean of X by c and the variance of X byc. That is, show that E(cX) = cE(X) and V(cX) = c³V(X).

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Answered: 5. Show that for a discrete uniform…

A First Course in Probability (10th Edition)

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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) = c°V(X).