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14. Do the following proofs. (a) If X is a discrete random variable and a > 0, prove that SD(aX) = a - SD(X). (SD' means standard deviation.)

14. Do the following proofs. (a) If X is a discrete random variable and a > 0, prove that SD(aX) = a - SD(X). (SD' means standard deviation.)

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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14. Do the following proofs. (a) If X is a discrete random variable and a > 0, prove that SD(aX) = a · SD(X). (SD' means standard deviation.) (b) Let X be a discrete random variable with E(X) = μ and Var(X) = o². Let X* X-#. (The random variable X* is called be the random variable defined by X* the standardized random variable of X.) 1. Prove that E(X*) = 0. 2. Prove that Var (X*) = 1. 15
Transcribed Image Text:14. Do the following proofs. (a) If X is a discrete random variable and a > 0, prove that SD(aX) = a · SD(X). (SD' means standard deviation.) (b) Let X be a discrete random variable with E(X) = μ and Var(X) = o². Let X* X-#. (The random variable X* is called be the random variable defined by X* the standardized random variable of X.) 1. Prove that E(X*) = 0. 2. Prove that Var (X*) = 1. 15
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