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5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y...
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0
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 pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).
X and Y are jointly uniformly distributed and their joint PDF is given by: fX,Y(x,y) = {k , 0<=x<=4, 0 <=y <= 8 0 , otherwise } a.) find the value of k that makes the joint PDF valid b.) compute the probability P[(X-2)^2 + (Y-2)^2 < 4] c.) compute the probability P[Y > 0.5X + 5]
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).
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
X and Y are jointly uniformly distributed and their joint PDF is given by: fX,Y(x,y) = {k , 0<=x<=4, 0 <=y <= 8 0 , otherwise } a.) find the value of k that makes the joint PDF valid b.) compute the probability P[(X-2)^2 + (Y-2)^2 < 4] c.) compute the probability P[Y > 0.5X + 5]
Let X and Y have the joint pdf fXY(x,y) = 24xy^3, 0<y<x<1. Find P(X>2/3, Y<1/3) Find P(X<2Y)
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)
Show all work! Thank you! 0<x<2, 0<y<1 23. The joint pdf of X and Y is fx.y(x, y)= (region below). 3 0 otherwise a) Determine f(y) b) Determine fx, (x) c) Determine E[Yx] d) Determine E[X|y] 0 1 2 24. Suppose that the joint probability density function of the jointly continuous random variables X and Y is x on the given region fxy(x,y)= 11 10 otherwise Determine fyly) 1 _$6x 0<x< y1 25. Let X and Y be continuous random...