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....
Student ID: Let the discrete RV X-UI-2,2]. Let Y X2 a) 14pts] What values X and Y can take? Find pdf's of both X and Y. b) [4pts] Compute the joint pdf, xy(x) c) [4pts] Compute the Ech) and Em d) [3pts] Compute the Cov(x.y e) [3pts] Compute the pxy Cor(x,Y). f) 2pts] Are X and Y independent? Prove it. Student ID: Let the discrete RV X-UI-2,2]. Let Y X2 a) 14pts] What values X and Y can take? Find...
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...
x>0,y>0. Problem 6 Consider the following joint pdf for the random variable X and Y where denotes a unit step function. (a) Find the constant C. (b) Find the marginal PDF's of X and Y. (c) Find the conditional PDF's fx(xY-y) and s, (ylX-x) (d) Find the conditional expected values, EX 1 Y = y} and EX X = Problem 6 Consider the following joint pdf for the random variable X and Y where denotes a unit step function. (a)...
Find the normalization constant c and the marginal pdf's for the following joint pdf fxy(x, y) = ce-*e-y for 0 Sysx < 0
Suppose X and Y have the joint pdf f (x, y) = 3y, 0 < y < 1, y − 1 < x < 1 − y 0 otherwise a) Give an expression for P (X > Y ). b) Find the marginal pdfs for Y . c) Find the conditional pdf of X given Y = y, where 0 < y < 1. d) Give an expression for E[XY ]. e) Are X and Y independent?
2. Let the pair (X,Y) have joint PDF fxy(x, y) = c, with 2.2 + y2 <1. (a) Find c and the marginal PDFs of X and Y. (b) What are the means of X and Y ? No calculations are needed, only a brief expla- nation is required. (c) Find the conditional PDF of Y given X = x and deduce E|Y|X = x]. (d) Obtain E(XY) and compare it to E[X]E[Y). (e) Are X and Y independent? Explain....
1. Determine the constant c such that the given function is a valid joint PDF for the jointly continuous random variables X and Y. f(x,y) ={cry otherwise 0 < y < 2x a. Find the value of the constant c. b. Find the marginal PDFs for X and Y. Are X and Y independent?
2. The joint pdf of random variables X and Y is given by f(x.y) k if 0 sysxs2 and f(x,y)-0 otherwise. a. Find the value of k b. Find the marginal pdfs of X and Y. Are X and Y independent? c. Find Covariance (X,Y) and Correlation(X,Y). Why cannot we say that X and Y have linear relation Yea X+ b, where a and b are real numbers?
Let X and Y have the joint pdf f(x,y) = e-x-y I(x > 0,y > 0). a. What are the marginal pdfs of X and Y ? Are X and Y independent? Why? b. Please calculate the cumulative distribution functions for X and Y, that is, find F(x) and F(y). c. Let Z = max(X,Y), please compute P(Z ≤ a) = P(max(X,Y) ≤ a) for a > 0. Then compute the pdf of Z.
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