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)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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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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