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1 Suppose that X is a continuous random variable with the density functions f(x) =a n2) for 1sx s2. Xisalso jointiy distributed with the continuous random variabieY, and the conditional density function of Y given X is fyx=x)=x-etor ISxs2 and y>0. Find the marginal density Tunction ofY.

1 Suppose that X is a continuous random variable with the density functions f(x) =a n2) for 1sx s2. Xisalso jointiy distributed with the continuous random variabieY, and the conditional density function of Y given X is fyx=x)=x-etor ISxs2 and y>0. Find the marginal density Tunction ofY.

MATLAB: An Introduction with Applications
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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**Transcription for Educational Website:** Suppose that \(X\) is a continuous random variable with the density function \(f(x) = \frac{1}{x \ln(2)}\) for \(1 \leq x \leq 2\). \(X\) is also jointly distributed with the continuous random variable \(Y\), and the conditional density function of \(Y\) given \(X\) is \(f(y|X = x) = x \cdot e^{-xy}\) for \(1 \leq x \leq 2\) and \(y > 0\). Find the marginal density function of \(Y\).
Transcribed Image Text:**Transcription for Educational Website:** Suppose that \(X\) is a continuous random variable with the density function \(f(x) = \frac{1}{x \ln(2)}\) for \(1 \leq x \leq 2\). \(X\) is also jointly distributed with the continuous random variable \(Y\), and the conditional density function of \(Y\) given \(X\) is \(f(y|X = x) = x \cdot e^{-xy}\) for \(1 \leq x \leq 2\) and \(y > 0\). Find the marginal density function of \(Y\).
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