Question 1 function given by Suppose that X and Y have a joint probability density ce if x, y ≥ 0 - {* 0 otherwise fx,y(x, y) = (a) Determine the value of the normalization constant c. (b) Find the marginal probability density function fx and state the name of the distribution of X. -3x-5y (c) Find the conditional probability density function fy|x=z. (d) Are the random variables X and Y statistically independent? Justify your answer. Consider now a different joint probability density function for X and Y, namely [12ye-3x-2y² 0 (e) What is the probability P(Y2 > 2X > 0) ? fx,y(x, y) = if x, y ≥ 0 otherwise

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