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Thread: Area under a curve

  1. #1 Area under a curve 
    Member epidecus's Avatar
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    Let's say I have some function continuous over all real numbers such that .

    How can I make it so that we know is a density curve?

    Imposing the condition that is even comes to mind. Does this work and what else can be said?
    Last edited by Markus Hanke; 11-19-2013 at 05:11 AM.
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  2. #2  
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    You need to define what you mean by density in this context.
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  3. #3  
    Member epidecus's Avatar
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    Sorry, it means to say a function in which the area under the entire curve is 1.

    Which, I guess, is the same as saying...

    .
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  4. #4  
    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by epidecus View Post
    Sorry, it means to say a function in which the area under the entire curve is 1.

    Which, I guess, is the same as saying...

    .
    Yes, this is very similar to the normalisation condition of a quantum wave function. What is your actual question ?
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    I don't know if this is the answer to your question (I don't understand very well the question) but you can say that function f(x) is a density function if f(x) is pairs (simmetric to the y axes)...because from what I understand you know that the area to 0 to infinity is 1/2
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  6. #6  
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    Quote Originally Posted by grimx View Post
    I don't know if this is the answer to your question (I don't understand very well the question) but you can say that function f(x) is a density function if f(x) is pairs (simmetric to the y axes)...because from what I understand you know that the area to 0 to infinity is 1/2
    Hmm, I thought as much. Thanks!

    Quote Originally Posted by Markus Hanke
    Yes, this is very similar to the normalisation condition of a quantum wave function. What is your actual question ?
    I honestly don't know what that is, though I have the suspicion that you think I'm disguising a homework question? If so, then I disagree. Since the time it was asked, I realized it doesn't make much sense. The only concrete thing that one can say is that f(x) is even.

    By the way, if it's not odd to ask, why was the original post's TEX code edited?
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    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by epidecus View Post
    I honestly don't know what that is, though I have the suspicion that you think I'm disguising a homework question?
    No, it is just that the integral you gave is similar in form to the normalisation conditin of a quantum wave function :

    Wave function - Wikipedia, the free encyclopedia

    By the way, if it's not odd to ask, why was the original post's TEX code edited?
    I took the liberty since the syntax of the original code was incorrect, so it didn't display at all. Hope you don't mind. I didn't change anything on the actual content, just on the syntax.
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  8. #8  
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    Quote Originally Posted by epidecus View Post
    Let's say I have some function continuous over all real numbers such that .

    How can I make it so that we know is a density curve?

    Imposing the condition that is even comes to mind. Does this work and what else can be said?
    In general a density function has the integral over the entire real line = 1 and f(x) ≥ 0 for all x. Even will work as long as the function is non-negative. However there are obviously many other ways.
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