3. (30 pts) Let X and Y be random variables of the continuous type having the...
4. Let X and Y be random variables of the continuous type having the joint pdf f(x,y) = 1, 0<x< /2,0 <y sin . (a) Draw a graph that illustrates the domain of this pdf. (b) Find the marginal pdf of X. (c) Find the marginal pdf of Y. (d) Compute plx. (e) Compute My. (f) Compute oz. (g) Compute oz. (h) Compute Cov(X,Y). (i) Compute p. 6) Determine the equation of the least squares regression line and draw it...
4. (25 pts, 25/6 pts each) Let X and Y be random variables of the continuous type having the joint p.d.f. f(x, y) = 8xy,0 £ x £ y £ 1. 1) Draw a graph that illustrates the domain of this p.d.f. 2) Calculate the marginal p.d.f.s of X and Y. 3) Compute 4) Compute 5) Write out the equation of the least squares regression line and draw it in a graph. 6) If your calculations are correct, in 3)...
4.4-14. Let X and Y be random variables of the continu- ous type having the joint pdf f(x,y) = 8xy, 0<xsys 1. Draw a graph that illustrates the domain of this pdf. (a) Find the marginal pdfs of X and Y. (b) Compute jx, My, o, oz, Cov(X,Y), and p. (c) Determine the equation of the least squares regres- sion line and draw it on your graph. Does the line make sense to you intuitively?
2. Let X and Y be continuous random variables having the joint pdf f(x,y) = 8xy, 0 <y<x<1. (a) Sketch the graph of the support of X and Y. (b) Find fi(2), the marginal pdf of X. (c) Find f(y), the marginal pdf of Y. () Compute jx, Hy, 0, 0, Cov(X,Y), and p.
(7 points) Suppose X and Y are continuous random variables such that the pdf is f(x,y) xy with 0 sx s 1,0 s ys 1. a) Draw a graph that illustrates the domain of this pdf. b) Find the marginal pdfs of X and Y c) Compute μΧ, lly, σ' , σ' , Cov(X,Y),and ρ d) Determine the equation of the least squares regression line and draw it on your graph. (7 points) Suppose X and Y are continuous random...
make sense to you intuitively? 4.4-14. Let X and Y be random variables of the continu- ous type having the joint pdf Draw a graph that illustrates the domain of this pdf (a) Find the marginal pdfs of X and Y. (b) Compute μχ, per, 07, σ3. Cov(X, Y), and p. (e) Determine the equation of the least square (c) Compute E that Y=y. (d) Find E(Y X (0, 1). Given t on the i y s t/2. sion line...
Let X and Y be jointly continuous random variables having joint density fxy(x,y) = 2 y + x1, x>0, y> O otherwise Find Cov(X,Y) and Determine the correlation coefficient PXY O A. Cov(X,Y) = -1/36 , PXY=-1/2 OB. Cov(X,Y) = -1/18, PXY= 1/3 OC. Cov(X,Y) = -1/36 , PXY=0 OD. Cov(X,Y) = 1/12, PXY--1/2
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
4. Let X and Y be continuous random variables with joint density function f(x, y) = { 4x for 0 <x<ys1 otherwise (a) Find the marginal density functions of X and Y, g(x) and h(y), respectively. (b) What are E[X], E[Y], and E[XY]? Find the value of Cov[X, Y]
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. 、