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Exercice 11. Let D be the unit disk in R$^2$, D = \{(x, y) \in R$^2$, x$^2$ + y$^2$ \le 1\}. Suppose X and Y have joint pdf f(x, y) = c if (x, y) \in D and zero otherwise. (a) Find c. (b) Find the marginal pdf $f_x$ and $f_y$. (c) Are X and Y independent? (d) Find E(X) and Var(X). (e) Find the covariance and correlation of X and Y. (f) Are X and Y uncorrelated?

          Exercice 11. Let D be the unit disk in R$^2$, D = \{(x, y) \in R$^2$, x$^2$ + y$^2$ \le 1\}. Suppose X and Y have joint pdf f(x, y) = c if (x, y) \in D and zero otherwise.
(a) Find c.
(b) Find the marginal pdf $f_x$ and $f_y$.
(c) Are X and Y independent?
(d) Find E(X) and Var(X).
(e) Find the covariance and correlation of X and Y.
(f) Are X and Y uncorrelated?

$Exercice 11. Let D be the unit disk in R^2, D = {(x, y) ∈R^2, x^2 + y^2 ≤1}. Suppose X and Y have joint pdf f(x, y) = c if (x, y) ∈D and zero otherwise. (a) Find c. (b) Find the marginal pdf fx and fy. (c) Are X and Y independent? (d) Find E(X) and Var(X). (e) Find the covariance and correlation of X and Y. (f) Are X and Y uncorrelated?$

Added by Jamie M.

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