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Suppose you have two independent random variables X ~ Exponential(A1) and Y Exponential(A2), A1 > 0, X2 > 0. Find: (a) The joint density function for (X,Y). (b) P (좋 >1. (c) P(X +Y > 1).

Suppose you have two independent random variables X ~ Exponential(A1) and Y Exponential(A2), A1 > 0, X2 > 0. Find: (a) The joint density function for (X,Y). (b) P (좋 >1. (c) P(X +Y > 1).

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
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Suppose you have two independent random variables X ~ Y ~ Exponential(A2), d1 > 0, 12 > 0. Find: Exponential(A1) and (a) The joint density function for (X,Y). (b) P (수 > 1). (c) P(X +Y > 1).
Transcribed Image Text:Suppose you have two independent random variables X ~ Y ~ Exponential(A2), d1 > 0, 12 > 0. Find: Exponential(A1) and (a) The joint density function for (X,Y). (b) P (수 > 1). (c) P(X +Y > 1).
Expert Solution
Step 1

X~Expλ1Y~Expλ2

Here, 

λ1>0 and λ2>0

It is given that X and Y are independent exponential random variables.

The marginal probability density function of X is given as:

fXx=1λ1e-xλ1;x>0=0               otherwise

The marginal probability density function of Y is given as:

fYy=1λ2e-yλ2;y>0=0               otherwise

 

 

 

 

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