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. 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...
The joint pdf is given. c(x + y2) for 0 SX S1 and 0 sys1 f(x,y) = 0 0.w. Find the conditional pdf of X given Y = y. (a) (b) Fim (r< 10-1)
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?
Q3. Suppose that X, Y have joint pdf a for x2 + y2 0 otherwise. 1. fxy(x, y)- (a) Find the value of a so that fxy(x, y) is a valid pdf. b) Find the marginal pdf for X Hint: It is helpful to sketch the region of the ry-plane where the pdf is non-zero
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...
Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is exponential with parameter equal to r (and mean 1/r) Note: Some useful integrals, for λ > 0: ar (a) Find the joint PDF of X and Y (b) Find the marginal PDF of Y (c) Find the conditional PDF of X, given that Y 2. (d) Find the conditional expectation of X, given that Y 2 (e) Find the...
0 〈 y 〈 x2く1· Consider two rvs X and Y with joint pdf f(x,y) = k-y, (a) Sketch the region in two dimensions where fx,y) is positive. Then find the constant k and sketch ) in three imesions Then find the constant k and sketch f(r.y) in three dimensions (b) Find and sketch the marginal pdf fx), the conditional pdf(x1/2) and the conditional cdf FO11/2). Find P(X〈Y! Y〉 1/2), E(XİY=1/2) and E(XIY〉l/2). (c) What is the correlation between X...
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....