4. Let X and Y be random variables of the continuous type having the joint pdf...
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?
(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...
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.
3. (30 pts) Let X and Y be random variables of the continuous type having the joint p.d.f 8 a) Draw a graph that illustrate the domain of this p.d.f. b) Find the marginal p.d.f.'s of X and Y. c) Compute μχ.Hr. d) Compute σ,, and σ e) Calculate Cov(X, Y) and p. x ?
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)...
All parts 3. Suppose X and Y are continuous random variables such that the pdf is f (x, y) 2(x y) with 0 s x sy s1 a) Draw a graph that illustrates the domain of this pdf b) Find the marginal pdfs of X and Y d) Determine the equation of the least squares regress ion line and draw it en rour grant
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 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. 、
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 following joint pdf f(x, y): y 0<1 and 0<y< 1 0 otherwise f(x,y) = Using the distribution method, find the pdf of Z = XY.