The Marginal pdf of a Function

In summary, the integral from 0 to infinity of xe^[-x(1+y)]dy can be simplified to -e^(-x) when plugging in 'b' for y, and becomes -e^(-x)*1 when plugging in zero for y. Another set of eyes helped spot this mistake.
  • #1
Shoney45
68
0

Homework Statement

The integral from 0 to infinity of xe^[-x(1+y)]dy



Homework Equations





The Attempt at a Solution


3105697.jpg


I can't figure out why the answer would be zero to a pdf. Also, for the indefinite integral the calculator produces the answer xy*e^(-x-xy). I cant' figure out how to get that answer, nor can I figure out if it would even matter if I was able to.

I guess I'm just asking for another set of eyes to look over my work and see if there is something that I am missing.
 
Physics news on Phys.org
  • #2
aren't you supposed to get -e^(-x)
?

when you plug 'b' into y, the term becomes zero.
but when you plug zero, it becomes -e^(-x)*1
 
  • #3
Roni1985 said:
aren't you supposed to get -e^(-x)
?

when you plug 'b' into y, the term becomes zero.
but when you plug zero, it becomes -e^(-x)*1

Yes! You're right! Something was bugging me about that big fat zero. I knew I needed another set of eyes. Thanks a lot!
 

Related to The Marginal pdf of a Function

1. What is the marginal pdf of a function?

The marginal pdf of a function is the probability density function (pdf) of one variable when all other variables are held constant. It represents the distribution of a single variable in a multivariate function.

2. How is the marginal pdf calculated?

The marginal pdf can be calculated by taking the integral of the joint pdf (the pdf of all variables) over all other variables except the one of interest. This results in a function of only the variable of interest, representing its marginal distribution.

3. What is the difference between a marginal pdf and a joint pdf?

A marginal pdf represents the distribution of one variable in a multivariate function, while a joint pdf represents the distribution of all variables together. The marginal pdf shows how the variable of interest is affected by the other variables, while the joint pdf shows how all variables are related to each other.

4. Why is the marginal pdf important in statistics?

The marginal pdf is important in statistics because it allows us to study the behavior of a single variable in a multivariate function. It can help us understand the relationship between variables and make predictions about the behavior of the variable of interest.

5. Can the marginal pdf be used to calculate probabilities?

Yes, the marginal pdf can be used to calculate probabilities. By integrating the marginal pdf over a certain range, we can find the probability of the variable of interest falling within that range. This can be useful in statistical analyses and decision making.

Similar threads

Marginal pdf, what am I doing wrong?
    • Calculus and Beyond Homework Help
Replies
5
Views
2K
Finding marginal distribution of 2d of probability density function
    • Calculus and Beyond Homework Help
Replies
6
Views
1K
Sinusoidal sequences with random phases
    • Calculus and Beyond Homework Help
Replies
1
Views
722
Marginal Probability Distribution
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Differential Equation ODE Solution help.
    • Calculus and Beyond Homework Help
Replies
3
Views
858
What is the Marginal PDF of X?
    • Calculus and Beyond Homework Help
Replies
4
Views
3K
Calculating C and Marginal PDFs for a Uniform Distribution on a Bounded Area
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Obtaining marginal PDFs from joint PDF
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Conquering the Integral of (1/x)*exp(-ax^2): A Scientific Inquiry
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Find Values of Osculating Circle Tangent to a Parabola
    • Calculus and Beyond Homework Help
Replies
4
Views
160

Hot Threads

Recent Insights

Back
Top