Suppose that X and Y have the joint density function f (x,
Chapter , Problem 15(choose chapter or problem)
Suppose that X and Y have the joint density function
\(f(x, y)=c \sqrt{1-x^{2}-y^{2}}, \quad x^{2}+y^{2} \leq 1\)
a. Find c.
b. Sketch the joint density.
c. Find \(P(X^2 + Y^2)\leq\) \(\frac{1}{2}\).
d. Find the marginal densities of X and Y. Are X and Y independent random variables?
e. Find the conditional densities.
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