Consider two continuous random variables X and Y characterized by the following joint probability density function
Consider two continuous random variables X and Y characterized by the following joint probability density function
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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Transcribed Image Text:Consider two continuous random variables X and Y characterized by the following joint
probability density function
fx.x(x, y) = ce (a#9), 0<x<y<+oo,
1 0, otherwise,
{
се
with a > 0, b > 0, c > 0.
Find the relationship between a, b, and c to make fx,y(x,y) a valid probability
density function.
a)
b)
Compute the marginal probability density function of X, and leveraging answer
in a), choose a, b, and c such that X is exponentially distributed with parameter
2 = 3, i.e. X ~ EXPO(3).
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