Using the method of transformations find the probability distribution of U=3Y-2 Let Y be a continuous random variable with probability density function3(y² + 2)0

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Using the method of transformations find the probability distribution of U=3Y-2

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Using the method of transformations find the probability distribution of U=3Y-2

Let Y be a continuous random variable with probability density function
3
(y² + 2)
0 <y< 2
f(y) =
elsewhere

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Expert Solution

Step 1

Let , X be the continuous random variable with pdf $f (y)$ then transformation of U = g(y) will have pdf is

$f (U) = f (g^{- 1} (u)) |\frac{d g^{- 1} (u)}{d u}| = f (g^{- 1} (u)) |\frac{d y}{d u}|$

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