make sense to you intuitively? 4.4-14. Let X and Y be random variables of the continu-...
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...
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...
4.4-2. Let X and Y have the joint pdf f(x, y) r + y, = x + y, (a) Find the marginal pdfs fx(t) and fy (v) and show that f(x,y)关fr (x)fy(y). Thus, X and Y are dependent. (b) Compute (i) μ x, (ii) μ Y. (111) 07, and (iv) 어.
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
Let X and Y be independent exponential random variables with pdfs f(x) = λe-λx (x > 0) and f(y) = µe-µy (y > 0) respectively. (i) Let Z = min(X, Y ). Find f(z), E(Z), and Var(Z). (ii) Let W = max(X, Y ). Find f(w) (it is not an exponential pdf). (iii) Find E(W) (there are two methods - one does not require further integration). (iv) Find Cov(Z,W). (v) Find Var(W).
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.
.1. Two discrete random variables X and Y are jointly distributed. The joint pmf is f(z, y) = 1/28 , SX = {0, 1, 2, 3, 4, 5,6}, and SY = {0, .... X), where Y is a non-negative integer a) Find the marginal pdfs of X and Y b) Caculate E(X) and E(Y). 2. Let the joint pdf of X aud Y be a) Draw the graph of the support of X and Y b) Determine c in the joint pdf. c) Find E(X +Y),...
4. Let X and Y be independent exponential random variables with pa- rameter ? 1. Given that X and Y are independent, their joint pdf is given by the product of the individual pdfs of X and Y, that is, fxy(x,y) = fx(x)fy(y) The joint pdf is defined over the same set of r-values and y-values that the individual pdfs were defined for. Using this information, calculate P(X - Y < t) where you can assume t is a positive...
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 ?