5.[20] For the following joint pdf, find c, and find μΧ, Hy, Ох, and Oy. f(x,y)-(cxy...
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.
3. (50 pts) Let (X, Y) have joint pdf given by c, y x, 0 < x < 1, f(x, y) 0, o.w., (a) Find the constant c. (b) Find fx(x) and fy (y) (c) For 0 < 1, find fyx=x(y) and pyjx=x and oy Y|X=x (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why.
Suppose the joint pdf of random variables X and Y is f(x,y) = c/x, 0 < y < x < 1. a) Find constant c that makes f (x, y) a valid joint pdf. b) Find the marginal pdf of X and the marginal pdf of Y. Remember to provide the supports c) Are X and Y independent? Justify
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
Let (X, Y) have joint pdf given by f(r, y)= < a, 0 < < 0, О.w., (a) Find the constant c (b) Find fx(x) and fy(y) (c) For 0 x< 1, find fyx=r (y) and py|x=x and oyx= (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why
Please do by hand. Thanks in advance. 5. Let X1 and X2 have joint pdf f(x1, x2) = 4xı, for 0 < x < x2 < l; and 0 otherwise. Find the pdf of Y = X/X2. (Hint: First find the joint pdf of Y and Y2 = X1.)
Let (X,Y) have joint pdf given by sey, 0 < x < y < 0, f(x, y) = { ( 0, 0.W., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
Let (X,Y) have joint pdf given by I c, \y < x, 0 < x < 1, f(x, y) = { | 0, 0.W., (a) Find the constant c. (b) Find fx(r) and fy(y) (c) For 0 < x < 1, find fy\X=z(y) and HY|X=r and oſ X=z- (d) Find Cov(X, Y). (e) Are X and Y independent? Explain why.