Answered: Show that if X is a discrete random…

Show that if X is a discrete random variable a mean of mu and a standard deviation sigma, then Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 1

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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Question

Show that if X is a discrete random variable a mean of mu and a standard deviation sigma, then

Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 1

Expert Solution

Step 1: Introducing the given information

$W e space h a v e space g i v e n space t h a t space X space i s space a space d i s c r e t e space r a n d o m space v a r i a b l e space w i t h space m e a n space o f space mu space a n d space s tan d a r d space d e v a i t i o n space o f space sigma i. e. E left parenthesis X right parenthesis equals mu S tan d a r d space d e v i a t i o n equals S D left parenthesis X right parenthesis equals sigma$

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Follow-up Question

In SD(X-mu/sigma)=1/sigma * SD(X)

What happened to the mean mu?

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