. For > 0 and A > 0, define the joint pdf -Ay = 0<x<A,<y, fx.y(,y)...
The joint pdf of X and Y is f(x, y) = x for x > 0, y > 0, x + y < 2. (a) Find P(Y > 2X). (b) Find E(XY). (c) Find P(0.7 < X < 1.71Y = 0.5).
7. Let X and Y have joint probability mass function fx.y(x,y) = (x+y)/30 for x = 0.1, 2.3 and y0,1,2. Find (a) PrX 2,Y-1) (b) PrX>2,Y S1) (c) Pr(X + Y=4) (d) Pr[X >Y) (e) the marginal probability mass function of Y, and (f) E[XY]
Consider the joint PDF of two random variables X and Y below. fx.y (x y) = 1, if 0 < x < 1, and 0 y< 1, and fxx (г, у) Oif andy are outside of that square. So, basically, the joint PDF is a constant over the unit square Let W X+Y. Suppose we express the CDF of W in the usual double integral form h Fw(W) 2 dy dx g where w-0.4 is a given value at which...
0 Sy s 1. Let X and Y have joint pdf: fx,y(x, y) = kx(1 – x)y for 0 < x < 1, (a) Find k. (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y. (d) Find Pſy < 81/2],P[X<Y]. (e) Are X and Y independent? (f) Find the correlation and covariance of X and Y. (g) Determine whether X and Y are uncorrelated. (h) Find fy(y|x) (i) Find E[Y|X = x]...
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.
2. Let X and Y be continuous random variables with joint pdf fx.y (x. y)- 3x, 0 Syx, 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?
Problem 3: X and Y are jointly continuous with joint pdf 0<x<2, 0<y<x+1 f(x,y) = 17 0, Elsewhere a) Find P(X < 1, Y < 2). b) Find marginal pdf's of X. c) f(x|y=1). d) Find E(XY). dulrahim
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
Let X and Y be a random variable with joint PDF: { ay fxy (x, y) x > 1,0 <y <1 0 otherwise x2, 1. What is a? 2. What is the conditional PDF fy\x(x|y) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of 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. 、