1. Let (X, Y) X, Y be two random variables having joint pdf f xy (xy)...
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.
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.
3). Let X and Y be two random variables with the joint pdf 41-, 0<b< 0<pく1; 6x f (,)0 elsewhere. ǐf 0 < z < 1; Find Pr(X >1/v=1). 3). Let X and Y be two random variables with the joint pdf 41-, 0
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. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(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. 、
3. Let f(x,y) = xy-1 be the joint pmf/ pdf of two random variables X (discrete) and Y (continuous), for x = 1, 2, 3, 4 and 0 <y < 2. (a) Determine the marginal pmf of X. (b) Determine the marginal pdf of Y. (c) Compute P(X<2 and Y < 1). (d) Explain why X and Y are dependent without computing Cou(X,Y).
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...
5. Suppose that the joint pdf of the random variables X and Y is given by - { ° 0 1, 0< y < 1 f (x, y) 0 elsewhere a) Find the marginal pdf of X Include the support b) Are X and Y independent? Explain c) Find P(XY < 1)
3. Consider two random variables X and Y with the joint probability density (a)o elsewhere which is the sane asin Question I. Now let Z = XY 2 and U = X be a joint transformation of (X, Y). (a) Find the support of (Z, U) (b) Find the inverse transformation (c) Find the Jacobian of the inverse transformation. (d) Find the joint pdf of (Z, U) (e) Find the pdf of Z XY from the joint pdf of (Z,...