The random variables X and Y have the joint density: fx,y(x,y) = 2-x-y, for 0
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- Let X and Y be independent random variables with density f (x) = 3x² for 0 < x < 1. Then P (X+ Y < 1) is equal toLet X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0.Let X and Y be random variables such that var(X) = and p = 16, var (Y) = 9, cor (X, Y) = -0.5. a. Find var(2X – 2Y + 10), b. Find cov(X – Y, X +Y).
- Two random variables X and Y have the joint pdf, f y(x, y) = Ae-ex+y), x, y 2 0 %3D = 0, elsewhere %3DThe joint probability function of two discrete random variables X and Y is given by f(x,y)=(1/42) (2x+y) where, x=0,1,2; y=0,1,2,3. Find P(x21, ys2). Use 4 decimal places.Let the joint density of random variables x and y be given by the following: fx,y(x, y) = 0.158(x + 1)8(y) + 0.18(x)8(y) + 0.18(x)8(y-2) +0.48(x - 1)8(y + 2) +0.28(x - 1)8(y-1) + 0.058(x - 1)8(y - 3) a) Determine the marginal density x and y of this joint density. b) Are these random variables statistically independent? Justify your answer. c) Find the marginal distribution functions for these random variables.
- The joint pdf of a bivariate random variable (X,Y) is given by Ske-(ax-by) x>0, y>0 fxy(x, y) = 0 otherwise where a and b are positive constants and k is a constant. Determine the value of k. (a) (b) Are X and Y independent?Let the random variables x and y have joint pdf as follows: f(x,y) = (11x² + 4y²), 0X is the Gaussian (μ=1, σ=2) random variable. Y is the Gaussian (μ=2, σ=4) radnom variable. X and Y are independent. a) What is the PDF of V = X + Y b) What is the PDF of W = 3X + 2YSEE MORE QUESTIONS