A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties.a. f(x, y) 2 0 for all (x, y)00Б.f(x, y) dA = 1-00с. P[(x, у) € R] -f(x, y) dAShow that the function is a joint density function and find the required probability.Osxs 2, 0 sysv?f(x, y) =0,elsewhereP(0 s xs 1, 0 sys 1)

Answered: Image /qna-images/answer/d188ca13-88a4-4867-b3a4-2c15e2d8e3f8.jpg

Answered: A joint density function of the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

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 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 uniformly distributed continuous random variable is defined by the density function f(x) = 0.2 on the interval [2, 7] . The value P(x > 4) = _____________. 0.1 0.2 0.4 0.6
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) = ______________________
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.
2. Let (X,Y) be a continuous bivariate random variable having the joint probability density function f(x,y) = cxy, 0≤x≤y≤2 for some real constant c. (e) Compute μX,μY ,σX2 ,σY2 ,Cov(X,Y), and ρ. (f) Find g(y|x = 12), the conditional probability density function of Y given X = 12. (g) Find P(Y > 34|X = 210
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 denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint densityf(x, y) = {?2 +??/3 ,0 < ? < 1, 0 < ? < 2, 0 elsewhere.a. Verify if it is a valid density function.b. Find P[(X, Y) ∈ A], where A = {(x, y) | 0 < x < ½, ¼ < y < ½.c. Find the marginal density g(x). d. Find the marginal density h(y).e. Find the conditional density f (x|y). f. Find the conditional density f (y|x). g. Find P(Y > 1 | X = ½). h. Find P(X > ½ | Y = 1). i. Determine if the random variables are statistically independent.
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)
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.
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]
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).

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS