Solution Found!
Suppose that Y is a normally distributed random variable
Chapter 4, Problem 181SE(choose chapter or problem)
Suppose that 𝑌 is a normally distributed random variable with mean \(\mu\) and variance \(\sigma^{2}\). Use the results of Example 4.16 to find the moment-generating function, mean, and variance of
\(Z=\frac{Y-\mu}{\sigma}\).
What is the distribution of 𝑍? Why?
Equation Transcription:
Text Transcription:
mu
sigma^2
Z=Y-mu over sigma
Questions & Answers
QUESTION:
Suppose that 𝑌 is a normally distributed random variable with mean \(\mu\) and variance \(\sigma^{2}\). Use the results of Example 4.16 to find the moment-generating function, mean, and variance of
\(Z=\frac{Y-\mu}{\sigma}\).
What is the distribution of 𝑍? Why?
Equation Transcription:
Text Transcription:
mu
sigma^2
Z=Y-mu over sigma
ANSWER:
Solution:
Step 1 of 3:
It is given that random variable Y is Normally distributed with mean and variance
.
Also, it is given that Z=
We need to find the moment generating function, mean and variance of Z and also we have to identify the distribution of Z.