6. Let the bivariate continuous random vector (X,Y) have the following joint probability density function: f(x, y) = {:

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6 Let The Bivariate Continuous Random Vector X Y Have The Following Joint Probability Density Function F X Y 1 (111.12 KiB) Viewed 28 times

6. Let the bivariate continuous random vector (X,Y) have the following joint probability density function: f(x, y) = {: C ‚0 ≤ y ≤1 − x² and − 1 ≤ x ≤ 1 0 otherwise 2 a. Graph the support on the two dimensional X-Y plane, and find the value of c. Hint: Integrate with respect to y first, dydx. b. Find the marginal probability density function of X, fx(x). c. Find the marginal probability density function of Y, fy(y). d. Find the conditional probability density function of X give Y=y, fx|y(x|y). e. Are X and Y independent? Why or why not.