Question 1 function given by Suppose that X and Y have a joint probability density ce-3r-5y if a, y 20 fx.x(x, y) = otherwise Wbatermine Deter the value of the normalization constant c. Find the marginal probability density function fx and state the name of the distribution of X. Y Find the conditional probability density function fyjx=z- (Y Are the random variables X and Y statistically independent? Justify your answer.

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Q: (d) Are the random variables X and Y independent? Justify your answer.

A: To check independence of X and Y we have to find marginal pdfs of X and Y.

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A: a. i. fZz = ∫x=-∞+∞fXxfYz-xdx          = ∫x=0x=z1×e-z-xdx,      0&lt;z≤1          = 1-e-z,    z≤0…

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