et X, Y have the joint pdf | cx for æ2 + y? < 1 and x > 0, y > 0 fx,Y O.w. here c is some constant. uestion part 1: (Answer by selecting the correct choices from the dropdown menus elow) le need to figure out the value of c. In order to do this, we need to evaluate the efinite double integral below, but first we need to figure out the limits of integration enoted by xlow, X'high, Ylow , Yhigh CUhigh Lhigh cx dxdy Ylow Jxlow ote that in the double integration above, we will do dx and then dy. I strongly ecommend that you use a piece of paper to sketch the support on the x, y plane. [ Select ] low = [ Select ] %3D high [ Select ] Cow =
et X, Y have the joint pdf | cx for æ2 + y? < 1 and x > 0, y > 0 fx,Y O.w. here c is some constant. uestion part 1: (Answer by selecting the correct choices from the dropdown menus elow) le need to figure out the value of c. In order to do this, we need to evaluate the efinite double integral below, but first we need to figure out the limits of integration enoted by xlow, X'high, Ylow , Yhigh CUhigh Lhigh cx dxdy Ylow Jxlow ote that in the double integration above, we will do dx and then dy. I strongly ecommend that you use a piece of paper to sketch the support on the x, y plane. [ Select ] low = [ Select ] %3D high [ Select ] Cow =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let X, Y have the joint pdf
for x? + y? < 1 and a > 0, y > 0
cx
fx,Y
0.W.
where c is some constant.
Question part 1: _(Answer by selecting the correct choices from the dropdown menus
below)
We need to figure out the value of c. In order to do this, we need to evaluate the
definite double integral below, but first we need to figure out the limits of integration
denoted by x1ow , Xhigh , Ylow » Yhigh
Xhigh
Suhish Soh ca dædy
Ylow
xlow
Note that in the double integration above, we will do dx and then dy. I strongly
recommend that you use a piece of paper to sketch the support on the x, y plane.
Xlow
[ Select ]
Xhigh
[ Select ]
%3D
[ Select ]
Ylow =
[ Select ]
Yhigh
%3D
Xlow
[ Select ]
[ Select ]
X high
sqrt( 1-y^2)
Ylow
- sqrt( 1 - y^2)
sqrt( 1 - x^2)
Yhigh
[ Select ]
Xlow
[ Select ]
X high
%D
[ Select ]
Ylow
sqrt( 1 - x^2 )
sqrt( 1-y^2 )
Yhigh =
%3D
1-y^2
1
Note that in the double integration above, we will do dx
recomr [Select ]
per to sketch the s
sqrt( 1 - x^2)
Xlow
Chigh
- sqrt( 1 - x^2)
Ylow
[ Select ]
%3D
Yhigh
%D
ISoloct 1
Xlow
[ Select ]
1
Xhigh =
sqrt( 1 - y^2)
sqrt( 1 - x^2)
Ylow =
%3D
Yhigh =
%3D
<>
>
>](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F419820c1-e9cd-469e-aa42-67c8a6edd9ca%2F095289cb-478e-4325-b502-20fd77edf20e%2Fe32tyaj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X, Y have the joint pdf
for x? + y? < 1 and a > 0, y > 0
cx
fx,Y
0.W.
where c is some constant.
Question part 1: _(Answer by selecting the correct choices from the dropdown menus
below)
We need to figure out the value of c. In order to do this, we need to evaluate the
definite double integral below, but first we need to figure out the limits of integration
denoted by x1ow , Xhigh , Ylow » Yhigh
Xhigh
Suhish Soh ca dædy
Ylow
xlow
Note that in the double integration above, we will do dx and then dy. I strongly
recommend that you use a piece of paper to sketch the support on the x, y plane.
Xlow
[ Select ]
Xhigh
[ Select ]
%3D
[ Select ]
Ylow =
[ Select ]
Yhigh
%3D
Xlow
[ Select ]
[ Select ]
X high
sqrt( 1-y^2)
Ylow
- sqrt( 1 - y^2)
sqrt( 1 - x^2)
Yhigh
[ Select ]
Xlow
[ Select ]
X high
%D
[ Select ]
Ylow
sqrt( 1 - x^2 )
sqrt( 1-y^2 )
Yhigh =
%3D
1-y^2
1
Note that in the double integration above, we will do dx
recomr [Select ]
per to sketch the s
sqrt( 1 - x^2)
Xlow
Chigh
- sqrt( 1 - x^2)
Ylow
[ Select ]
%3D
Yhigh
%D
ISoloct 1
Xlow
[ Select ]
1
Xhigh =
sqrt( 1 - y^2)
sqrt( 1 - x^2)
Ylow =
%3D
Yhigh =
%3D
<>
>
>
Transcribed Image Text:Question part 2:
What is the value of c that makes this a proper joint distribution (i.e. integrates to 1
over the support)?
O 3/2
O 1/3
O 3
O We do not have enough information to answer this question.
Question part 3:
find fx (x), the marginal distribution of X. (Answer choices are given in terms of c)
O fx(x) = cx/1 – x²
for 0 < x < 1, and O otherwise
O fx(x) = ;(1 – y?) for 0 < x < /1- y², and O otherwise
O fx(x) = c(1 – y²) for 0 < x < 1, and O otherwise
O fx(x) = cx 1 – x²
for 0 <x < V/1 – y², and O otherwise
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman