2-3.4 a) A random variable Y is related to the random variable X of Problem 2-3.3 by Y = 3X -4. Find the probability density function of the random variable Y. b) Find the probability that Y is negative. c) Find the probability that Y is greater than X.

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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Problem 2-3.3. But change the problem to say f_X(x)=A/(1+x^2).

 

I only need the Answer for Problem 2-3.4. Use the changes made in Problem 3.

2-3.3 a) A random variable X has a probability density function of the form
fx(x) = exp(-2|x|)
-∞ < x <∞
A second random variable Y is related to X by Y = X². Find the probability density
function of the random variable Y.
b) Find the probability that Y is greater than 2.
2-3.4 a) A random variable Y is related to the random variable X of Problem 2-3.3 by
Y = 3X - 4. Find the probability density function of the random variable Y.
b) Find the probability that Y is negative.
c) Find the probability that Y is greater than X.
Transcribed Image Text:2-3.3 a) A random variable X has a probability density function of the form fx(x) = exp(-2|x|) -∞ < x <∞ A second random variable Y is related to X by Y = X². Find the probability density function of the random variable Y. b) Find the probability that Y is greater than 2. 2-3.4 a) A random variable Y is related to the random variable X of Problem 2-3.3 by Y = 3X - 4. Find the probability density function of the random variable Y. b) Find the probability that Y is negative. c) Find the probability that Y is greater than X.
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