Simple marginal distribution problem

In summary, Nate is trying to say that the function only exists on a certain interval, and that if y goes to negative infinity, the integral becomes infinite.
  • #1
FunkyDwarf
489
0
Hey guys,

Doin revision for my maths exam and i came across this question from a past exam:

Homework Statement


Find fx(x,y) of
[tex]f(x,y) = \frac{(1+4xy)}{2} for 0 \leq x, y \leq 1[/tex] and zero otherwise

Homework Equations


Now this should equal[tex] \int \frac{(1+4xy)}{2} dy [/tex]over all y but that leads to infinities ( as y goes from minus infinity to 1)which obviously we can't have. I am sure I am missing something simple and stupid i just need someone to point ito out :)

Cheers
-G

NOTE: Sorry this latex is stuffing up, tryin to fix it
 
Last edited:
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  • #2
You might want to split the integral into a couple of pieces. Remeber:
[tex]f(x,y) \neq \frac{1+4xy}{2}[/tex]
 
  • #3
I think what Nate is trying to say is that f(x,y) is only defined on a certain domain. Since f(x,y) is a pdf, y cannot be arbitrarily negative as this would make f(x,y) negative. Remember, the integral of f(x,y) over the domain must be 1.

Try to make sense of your domains. Draw them. X and Y can sometimes be dependant on each other...which can make things complicated.
 
  • #4
Doesn't this expression,

[tex]0 \leq x, y \leq 1[/tex]

mean x and y are both in [0,1]? If y runs to minus infinity the question doesn't make much sense.
 
  • #5
ZioX said:
I think what Nate is trying to say is that f(x,y) is only defined on a certain domain. Since f(x,y) is a pdf, y cannot be arbitrarily negative as this would make f(x,y) negative. Remember, the integral of f(x,y) over the domain must be 1.

Actually, [itex]f(x,y)[/itex] is only non-zero on a certain domain, it's defined on the entire plane.
 
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  • #6
A good thing to do, is first draw your "support". Sketch where the function is non-zero. This allows you to easily setup the bounds on the integral.
 
  • #7
NateTG said:
Actually, [itex]f(x,y)[/itex] is only non-zero on a certain domain, it's defined on the entire plane.

Oh come on! Grant me some liberties. Although you're right, I probably shouldn't have used those words.
 
  • #8
Ah of course! i did draw it, i just drew it wrong :P thanks guys
 

What is a simple marginal distribution problem?

A simple marginal distribution problem is a statistical problem where the goal is to calculate the probability of a single event occurring, given the probabilities of all possible combinations of events.

How is a simple marginal distribution problem different from a conditional probability problem?

A simple marginal distribution problem only considers the probabilities of individual events occurring, while a conditional probability problem takes into account additional information or conditions.

How do you calculate a simple marginal distribution?

To calculate a simple marginal distribution, you need to determine the probability of each individual event and add them together. This will give you the total probability of the event occurring.

What is the purpose of a simple marginal distribution?

The purpose of a simple marginal distribution is to understand the likelihood of a single event occurring in a larger set of possible events. It can also be used to compare the relative frequencies of different events.

What are some real-world applications of simple marginal distribution?

Simple marginal distribution can be applied in various fields such as economics, biology, psychology, and social sciences. It can help to analyze consumer behavior, understand patterns in disease outbreaks, and study human decision-making processes.

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