Calculating Limits of Integration for Joint Distributions

Click For Summary
SUMMARY

The discussion focuses on calculating the limits of integration for joint distributions, specifically the double integral ∫_{0}^{1}∫_{1-y}^{1} ce^x e^y dx dy. The user seeks confirmation on their interpretation of the limits and guidance on how to calculate them. The correct limits are confirmed, and the discussion emphasizes the importance of graphing the region defined by the lines x=1, y=1, and x+y=1 to visualize the integration area.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with joint distributions in probability theory
  • Knowledge of graphing linear equations
  • Basic proficiency in exponential functions
NEXT STEPS
  • Study the properties of joint distributions in probability
  • Learn how to graph regions defined by inequalities
  • Explore the application of double integrals in calculating probabilities
  • Investigate the use of software tools like MATLAB for visualizing integrals
USEFUL FOR

Students and professionals in mathematics, statistics, and data science who are working with joint distributions and double integrals, particularly those looking to enhance their understanding of integration limits and graphical representations.

sid9221
Messages
110
Reaction score
0
http://dl.dropbox.com/u/33103477/Joint.png

This is my interpretation of the limits of integration can you tell me if this is correct and also how do you calculate these limit's. Cause I'm not completely sure how they're calculated.

\int_{0}^{1}\int_{1-y}^{1} ce^x e^y dx dy
 
Last edited by a moderator:
Physics news on Phys.org
Yes, that is correct. Now what is the graph of that region?
Draw the lines x= 1, y= 1, x+ y= 1.
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
Replies
21
Views
2K
  • · Replies 16 ·
Replies
16
Views
3K