Problem 3: (15 points) The random variables X and Y have the joint PDF otherwise 1)...
X and Y are random variables with the joint PDF fx.^(t,y)-65536 0 otherwise. (a) What is the marginal PDFfx(x)? ㄑㄨ 8 5xA4/65536 fx(x) 0 otherwise (b) What is the marginal PDF fy(v)? (5 * 843)/(3*655 0 〈y〈 64 fy(y) = 0 otherwise
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
7.5.6 Random variables X and Y have joint PDF fx,y(x, y) = _J1/2 -1 < x <y <1, 1/2 10 otherwise. (a) What is fy(y)? (b) What is fx|v(x\y)? (c) What is E[X|Y = y)?
Suppose that X and Y are random variables the following joint PDF: fxy(x,y) = otherwise Determine fx, the marginal PDF of X. a. etermine Fx, the marginal CDF of X.
4.5.4 X and Y are random variables with the joint PDF ( 5x2/2 JX,Y (x, y) = -1 < x < 1; 0 <y < x2, otherwise. 10 (a) What is the marginal PDF fx(x)? (6) What is the marginal PDF fy(y)?
7. The joint pdf of two random variables X and Y is given by 0sxs3,0s y<5 fx(x,y) 15' 0, otherwise Find Cov(X,y)
1. Consider a pair of random variables (X, Y) with joint PDF fx,y(x, y) 0, otherwise. (a) 1 pt - Find the marginal PDF of X and the marginal PDF of Y. (b) 0.5 pt - Are X and Y independent? Why? (e) 0.5 pt - Compute the mean of X and the mean of Y.
Problem #5 (20 points) - Quotient of Two Random Variables Suppose that X and Y are independent positive continuous random variables with pdfs fx(x) and fy (y) and suppose that Z = X/Y. Show that the pdf of Z can be computed from the pdfs fx(x) and fy(y), using fz(2) = fx(yz)fy(y)ydy.
3. The joint pdf for random variables X and Y is given by 0 otherwise Calculate E(X) by conditioning ( EX|-1, EXİY-ијЛ,(y)dy )
2. Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y ≤ 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y |X = x. (d) Find P(Y < 3|X = 1). Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...