2. Let the joint pdf of X and Y be given by f(xy)-cx if 0sysxsi Determine that value of c that makes f into a valid pdf. a. Find Pr(r ) b 2 C. Find Prl X d. Find the marginal pdf's of X and Y e. Find the conditional pdfs of 자리 and ri- f. Are X and Y independent? Give a reason for your answer g. Find E(X), E(Y), and E(X.Y)
2. Let the joint pdf of X...
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
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
Problem 2. Assume a random vector (X Y with cdf F(r, ) and pdf f(r,y) (i) Show that Y/X has the pdf f(x, z) |da, g(z) = (ii) For X and identify the distribution of this pdf. xt independent, evaluate the pdf of Y/VX N(0, 1) and 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. 、
The joint pdf is given.
c(x + y2) for 0 SX S1 and 0 sys1 f(x,y) = 0 0.w. Find the conditional pdf of X given Y = y. (a) (b) Fim (r< 10-1)
1. (10 pts) Let the joint pdf of X and Y be f(x, y) = x + cy2 , 0 ≤ y ≤ x ≤ 1 a) Draw the graph of the support of X and Y . b) Determine c in the joint pdf. c) Find E(X + Y ), where X + Y ≤ 1.
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.
9. Let y= X2, where X has the pdf below (a) Find the mean of Y without finding the pdf of Y. (b) Write the pdf of Y:f<v). (c) Find the mean of Y using.ffy), confirming your answer in part (a).
1. For pdf f (r, y) = 1.22, 0 < x < 1,0 < y < 2, z +y > 1, calculate: EY) and () E (X2)