Consider two continuous random variables X and Y characterized by the following joint probability density function 1. S ce-(ax+by), 00, b > 0, c> 0. Find the relationship between a, b, and c to make fx,y(x,y) a valid probability density function. а) 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). b)

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Consider two continuous random variables X and Y characterized by the following joint
probability density function
1.
ce-(ax+by),
0, otherwise,
се
0<x<y<+o,
fxx(x,y) = {
with a > 0, b > 0, c > 0.
Find the relationship between a, b, and c to make fx̟y(x, y) a valid probability
density function.
a)
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).
b)
Transcribed Image Text:Consider two continuous random variables X and Y characterized by the following joint probability density function 1. ce-(ax+by), 0, otherwise, се 0<x<y<+o, fxx(x,y) = { with a > 0, b > 0, c > 0. Find the relationship between a, b, and c to make fx̟y(x, y) a valid probability density function. a) 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). b)
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