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**Statsnoob2718** Suppose the sample space of the random variables X and Y is 0 < x < 1 and $\displaystyle x^2$ < y < 1. Let f (x, y) = c on this sample space, and 0 elsewhere.

(a) Sketch the sample space.

This is a bivariate distribution so it's a table with an X axis from 0 to 1 but i'm not sure about the y-axis?

(b) Determine the constant c.

does the probability always add up to one?

(c) Calculate $\displaystyle f_X$ (x) and $\displaystyle f_Y$ (y)

(d) Are X and Y independent?

(e) Find P (X > Y )