A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties.а. f(x, у) 2 0 for all (x, y)b.f(x, у) dA 3D 1с. Р[(х, у) E R] 3f(x, у) dAShow that the function is a joint density function and find the required probability.f(x, у) %3DExy, 0 sxs 2, 0 < y s V66elsewhereP(0 < x s 1, 0 < y< 2)

Given: fx,y=16xy0≤x≤2, 0≤0y≤60elsewhereP0≤x≤1, 0≤y≤2 We have to prove that given function is joint…

Answered: A joint density function of the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

The random vector (X, Y ) has the following joint probability density function:f(X,Y )(x, y) = 4xye^−(x2+y2), x > 0, y > 0,0 , otherwiseLet Z =√(X^2 + Y ^2) . Find the probability density of the random variable Z.
A continous random variable X has the density function. f(x) = {x, 0 < x ≤ 1, {2 − x, 1 < x ≤ 2, {0, elsewhere. (a) Show that P(0 < X < 2) = 1 (b) Find P(X < 1.2)
The joint density of X and Y is given by f(x,y) = e-(x+y) for 0<x<∞,0<y<∞ and 0 otherwise Find the density function of the random variable Z=X/Y.
For random variables X and Y with joint density function f(x,y) = 6e-2x-3y. (x,y > 0) and f(x,y) = 0, otherwise, find: a) P(X <= x, Y <= y) b) fx(x) c) fy(y) d) Are X and Y independent? Give a reason for your answer.
Consider the function Find the relationship between the positive constants a and k such that f is a joint density function of the continuous random variables x and y
Given the density function of the random variables (X,Y) as f(x,y)=3x2y+ 3xy2 , for 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 = 0 otherwise Find the marginal and conditional density functions. Also find the conditional probability P [1/2 ≤ x ≤ 3/4 | 1/2 ≤ Y ≤ 2/3]
The joint probability density function of random variable X and Y is given by: f(x,y) = {e^-y, if 0<x<y<∞ 0, otherwise}LEt Z=X+Y, Find the probability density function of Z.
The random variables X and Y have a joint density function f(x, y). f(x,y)= 2x+2y 0<x<1, 0<y<1, y>x 0 elsewhere P(X < 0.5, Y < 0.5) = ______________________
1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.
Let X and Y be independent uniform random variables on (0, 1). Find their joint density function f (x, y). Use the joint density function to calculate the probability P(X < Y).
The joint probability mass function of the two random variables (X, Y) is given by f(x,y) = { 1/5(3x-y), 1<=x<=2 , 1<=y<=3 0 , otherwise• Find the P( X ≤ Y)• Find the marginal density functions of X and Y• Are X and Y independent?• Find E(XY)
Let X and Y be two continuous random variables with joint probability density function f(x,y) = k(x + y) for 0 < x < 1, 0 < y < 1 and 0 otherwise, where k is a constant. Find the marginal probability density functions of X and Y.

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