Question: Joint distributions: Let a random point (X ,Y) have the uniform distribution over the unit disk S a) Sketch the support and graph the density;

Joint distributions:

Let a random point (X ,Y) have the uniform distribution over the unit disk S a) Sketch the support and graph the density; b) Find P(X + Y > 0) and P(| X | + | Y | 1) ; c) Find the marginal distributions; d) Find the correlation coefficient; e) Find the conditional expectation E[ X | Y =1/2] and conditional variance E[X | Y = 0] .

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