Ques: Option B is correct.
7.695 points Save Answer QUESTION 4 Let the random variable X and Y have the joint...
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
4. Let X and Y have joint density function le-x 0 < y < x < 0 Jxy(x, y) = lo elsewhere Another random variable of interest is U=X–Y. Find the probability density function for U.
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
2. Let the random variables X and Y have the joint PDF given below: 2e -y 0 xyo0 fxy (x, y) otherwise 0 (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 X and Y be continuous random variables with joint distribution function: f(x,y) = { ** 0 <y < x <1 otherwise What is the P(X+Y < 1)?
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )
Let X and Y be random variables with joint density function f(x,y) бу 0 0 < y < x < 1 otherwise The marginal density of Y is fy(y) = 3y (1 – y), for 0 < y < 1. True False
3. (16 points) Suppose that X and Y have the following joint p.d.f. f(x,y) = for 0 < x < y,0 < y <, y 0 otherwise. Compute E[X2]y], the expectation of the conditional distribution of x2 given Y = y.
2. Let the random variables X and Y have the joint PDF given below: S 2e-2-Y 0 < x < y < fxy(x,y) = { 0 otherwise (a) Find P(X+Y < 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y|X = r. (d) Find P(Y <3|X = 1).
Let X and Y be continuous random variables with joint pdf fx.v (x, y)-3x, OSysx<1, and zero otherwise. a. b. c. d. e. What is the marginal pdf of X? What is the marginal pdf of Y? What is the expectation of X alone? What is the covariance of X and Y? What is the correlation of X and Y?