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)
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...
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.
Problem 3 Let X and Y have joint pdf: fxy(x, y) = k(x + y) for 0 sxs1,0 s y s 1. (a) Find k. (b) Find the joint cdf of (X, Y). (c) Find the marginal pdf of X and of Y. (d) Find P[X < Y), P[Y < X²), P[X + Y > 0.5). (a) Find E[(X + Y)?]. (b) Find the variance of X + Y. (c) Under what condition is the variance of the sum equal...
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...
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)
2. Suppose X and Y have the joint pdf fxy(x, y) = e-(x+y), 0 < x < 00, 0 < y < 0o, zero elsewhere. (a) Find the pdf of Z = X+Y. (b) Find the moment generating function of Z.
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 two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
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....
5. The joint PDF of X and Y is given by s 3 fxy(x, y) = 3 o 0<x<3, 1<y<2, otherwise. Determine P[X<Y]. (8 pts)
* The joint pdf of x and Y is Fxy (x,y) = cx^3 y , 0 <x<y<1 . A) find the value of C to make this a valid pdf? * The proportion of defective parts shipped by a wholesaler varies from shipment to shipment. Suppose that the proportion of defective in shipment follow a beta distribution with a=4 and B = 2 . A) what is the probability that a shipment will have fewer than 20% defective parts ?