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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

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

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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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
Transcribed Image Text: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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