Let the random variable X and Y have the joint pmf $\qquad f(x, y) = \frac{x^2 y^2}{c}, x = 1, 2; y = 1, 2, 3$ and c > 0. a. Find c. b. Find $\mu_x$. c. Find $\mu_y$. d. Find $\sigma_x^2$. e. Find $\sigma_y^2$. f. Find Cov(X, Y). g. Find $\rho$, Corr(X, Y). h. Are X and Y independent? i. Find Var(X|Y = 2).
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We have f(1,1) + f(1,2) + f(1,3) + f(2,1) + f(2,2) + f(2,3) = 1 c(1*1 + 1*2 + 1*3 + 2*1 + 2*2 + 2*3) = 1 c(1 + 2 + 3 + 2 + 4 + 6) = 1 c(18) = 1 c = 1/18 Show moreā¦
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