×
Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 3.3 - Problem 10e
Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 3.3 - Problem 10e

×

# If X is N(?, ? 2 ), show that the distribution of Y = aX +

ISBN: 9780321923271 41

## Solution for problem 10E Chapter 3.3

Probability and Statistical Inference | 9th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Probability and Statistical Inference | 9th Edition

4 5 1 264 Reviews
24
4
Problem 10E

Problem 10E

If X is N(μ, σ 2 ), show that the distribution of Y = aX + b is N(+ b, a2σ 2 ), a ≠ 0. Hint: Find the cdf P(Y y) of Y, and in the resulting integral, let w = ax+b or, equivalently, x = (w b)/a.

Step-by-Step Solution:

Step 1 of 2 :

A random variable X is  normally distributed with mean  and standard deviation  .

The probability density function is

f(x) =

The claim is to show that the distribution of Y = ax+b is N(), a

Where, P(Xx) =  dt

Step 2 of 2

#### Related chapters

Unlock Textbook Solution