Explain in detials. Thank you! 1. A random variable $ X $ has expectation $ E(X) = \mu $ and variance $ \sigma^2 $. Suppose that $ Z = \frac{X - \mu}{\sigma} $.(a) Compute $ E(Z) $.(b) Compute $ \text{Var}(Z) $ and $ \sigma(Z) $.

Given that X is a random variable with expectation and variance .Suppose that

Answered: 1. A random variable X has expectation…

Math

Probability

1. A random variable X has expectation E(X) = μ and variance o². Suppose that Z = a) Compute E(Z). X-μ X-H. σ

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

Explain in detials. Thank you!

1. A random variable $ X $ has expectation $ E(X) = \mu $ and variance $ \sigma^2 $. Suppose that $ Z = \frac{X - \mu}{\sigma} $.

(a) Compute $ E(Z) $.

(b) Compute $ \text{Var}(Z) $ and $ \sigma(Z) $.

Expert Solution

Step 1: Given information:

Given that X is a random variable with expectation $E open parentheses X close parentheses equals mu$ and variance $V open parentheses X close parentheses equals sigma squared$ .

Suppose that $Z equals fraction numerator X minus mu over denominator sigma end fraction$

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