Question

The joint distribution of X and Y is defined by cf(x,y)f(x)f(y)V(x) 1. The joint distribution of X and Y is defined by 0 < x < 1, 0 < y < 3 otherwise f(x,y) a. Find c to verify that f(x,y) is a joint probability density function b. Find f(x) c. Find f(y) d. Find fX|0 < y < 1 e. Find fY|0 < x < 0.5 f. V(X)

          The joint distribution of X and Y is defined by
cf(x,y)f(x)f(y)V(x)
1. The joint distribution of X and Y is defined by
0 < x < 1, 0 < y < 3 otherwise
f(x,y)
a. Find c to verify that f(x,y) is a joint probability density function
b. Find f(x)
c. Find f(y)
d. Find fX|0 < y < 1
e. Find fY|0 < x < 0.5
f. V(X)
        
Show more…
the joint distribution of x and y is defined by cfxyfxfyvx 1 the joint distribution of x and y is defined by 0 x 1 0 y 3 otherwise fxy a find c to verify that fxy is a joint probability dens 45885

Added by William M.

Close

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
The joint distribution of X and Y is defined by cf(x,y)f(x)f(y)V(x) 1. The joint distribution of X and Y is defined by 0 < x < 1, 0 < y < 3 otherwise f(x,y) a. Find c to verify that f(x,y) is a joint probability density function b. Find f(x) c. Find f(y) d. Find fX|0 < y < 1 e. Find fY|0 < x < 0.5 f. V(X)
Close icon
Play audio
Feedback
Powered by NumerAI
Danielle Fairburn Kathleen Carty
Jennifer Stoner verified

Sri K and 91 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
the-joint-probability-density-function-of-x-and-y-is-given-by-fxy-cy-zx-ev-sxy0y-find-6-find-the-marginal-densities-of-x-and-y-the-joint-probability-density-function-of-x-and-y-is-given-by-f-32056

The joint probability density function of X and Y is given by fxy) = c(y - zx) e^(-sx) for 0 < y < x < 1 Find c. Find the marginal densities of X and Y: The joint probability density function of X and Y is given by fxy) = x + (xy/3) for 0 < x < 1 and 0 < y < 2 Verify that this is indeed a joint density function. b) Compute the density function of X. Find P(X < Y). Find P(Y > (2/4)X). Find E[X].

Sri K.

suppose-x-and-y-have-joint-density-function-3-ry-yp-if-0-x-2-0-y-1-fxxxy-1-0-otherwise-sketch-the-support-of-joint-distribution-x-y-b_-check-that-f-is-a-genuine-joint-density-function-find-t-41933

Suppose X and Y have joint density function f_X,Y(x,y) = { 3/5(xy + y^2) if 0 <= x <= 2, 0 <= y <= 1, 0 otherwise. a. Sketch the support of joint distribution (X, Y) b. Check that f is a genuine joint density function. c. Find the marginal density functions of X and Y. d. Calculate the probability P(X < Y). e. Calculate the expectation E[XY]. f. Determine whether X and Y are independent.

Adi S.

suppose-x-and-y-have-joint-density-function-3xy-yp-if-0-x-2-0-y-1-fxxxy-0-otherwise-a_-sketch-the-support-of-joint-distribution-x-y-b_-check-that-f-is-a-genuine-joint-density-function-c_-fin-25226

Suppose X and Y have joint density function f_{X,Y}(x,y) = { 3/5(xy + y^2) if 0 ≤ x ≤ 2, 0 ≤ y ≤ 1 0 otherwise a. Sketch the support of joint distribution (X, Y) b. Check that f is a genuine joint density function. c. Find the marginal density functions of X and Y. d. Calculate the probability P(X < Y). e. Calculate the expectation E[XY]. f. Determine whether X and Y are independent.

Adi S.


*

Recommended Textbooks

-
Elementary Statistics a Step by Step Approach

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition
achievement 1,005 solutions
The Practice of Statistics for AP

The Practice of Statistics for AP

Daren S. Starnes, Daniel S. Yates, David S. Moore 4th Edition
achievement 1,530 solutions
Introductory Statistics

Introductory Statistics

Barbara Illowsky, Susan Dean 1st Edition
achievement 1,794 solutions

*

Transcript

-
00:01 Given f of x comma y is equal to c of y square minus x square multiplied by e power minus y, where x varies from minus y to plus y and y varies from 0 to infinity.
00:23 So first we are going to calculate the value of c, that is double integral minus infinity to infinity, x comma y, d x, dy is equal to 1.
00:38 Now applying the corresponding values, it will be in terms of integral minus infinity to infinity, sorry, 0 to infinity.
00:47 Then it will be minus y to y.
00:51 C multiplied by x square minus y square, sorry, y square minus x square, multiplied by e power minus x squared, multiplied by e power minus y, multiplied by d, multiplied by d, x, dy is equal to 1.
01:07 So first integrating the inner most part, it will be c, multiplied by integral over 0 to infinity, in terms of integral minus y to y, y square minus x square, multiplied by e power minus y, d x, multiplied by d, y, is equal to y.
01:36 On solving this, integrating the innermost part, we will be obtaining the solution to be 2y cube, e power minus y, minus 2 y, 2, ype, e power minus y, divided by 3, which is equal to.
01:56 So on simplifying further, we will be obtaining 4c3 multiplied by integral 0 to infinity, y cube, e power minus 1 .5.
02:10 Multiplied by d .y is equal to 1...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever