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Jointly Distributed Random Variables : Joint Probability Density Functions

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Suppose X and Y are jointly continuous with joint pdf f(x,y)=xe^[-x(1+y)], x,y>0.

a) What are the marginal pdf's of X and Y?
b) What is the conditional pdf of X given Y=y?
c) What is the conditional pdf of Y given X=x?
d) What is the distribution of Y given X=x called?

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Joint Probability Density Functions are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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Marginal and Conditional Random Variables

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Let X and Y be two jointly distributed random variables having joint pdf

What is the marginal pdf fX(x)? What is the conditional pdf fY(y|{X=x})? Are X and Y statistically independent? Are X and Y uncorrelated?

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