Given,
(a)
E(XY)
E(XY) = 1/6
(b)
E(X) = 1/4
(c)
Cov(X,Y) = E(XY) - E(X) E(Y)
E(Y) = 1/2
Cov(X,Y) = E(XY) - E(X) E(Y) = 1/6 - (1/4)*(1/2) = 1/6 - 1/8 = 1/24
Cov(X,Y) = 1/24
Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o< <p (a) Find E[XY]...
Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o< <p (a) Find E[XY] (b) Find E[X] (c) Find the Covariance of X and Y Problem 4 Suppose X and Y have joint PDF Ixr(zy)-{0,y, otherwise, o
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)?
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
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...
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than...
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 < x < 1,0 < y< 1 a) Find k. b) Find the joint cdf of X and Y. c) Find the marginal pdf of X and Y. d) Find P(Y < VX) and P(X<Y). e) Find the correlation E(XY) and the covariance COV(X,Y) of X and Y. f) Determine whether X and Y are independent, orthogonal or uncorrelated.
Let X and Y have joint pdf f(x, y)= e if 0 < x < y< o and zero otherwise. Find Е(X |у). 16.
Suppose X, Y are random variables whose joint PDF is given by . 1 0 < y < 1,0 < x < y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
18. LetX and Y have joint pdf/(x, y) = eッ. 0 < x < y < oo and zero otherwise. (a) Find the joint pdf of S = X + Y and T-X. (b) Find the marginal pdf of T (c) Find the marginal pdf of S.
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?