The expected value E (X) of a discrete probability distribution is u 13 A constant a is added to all the values in the distribution. Let the random variable of this new a distribution be Z, so that Z = X + a. Show that the expected value E (Z) of the new distribution is u + a. b Each value in the distribution is multiplied by a constant k. Let the random variable of this new kX. Show that the expected value E (Z) of the new distribution is ku. distribution be Z, so that Z You have now proven that for all constants k and a, E (kXa) kE(X) a

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