Integral or probability question

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    Integral Probability
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The discussion centers on the property of probability density functions (PDFs) and their integrals. Specifically, it confirms that if the integral of a PDF, denoted as P(x), equals 1, then the transformation P(kx) results in the integral \int^{\infty}_{-\infty}P(kx)dx=\frac{1}{k} for any constant k. This property holds true for all improper integrals from -∞ to under the condition that the original integral evaluates to 1.

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Boxc
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Hello,

I came across a text saying that if
[tex]\int^{\infty}_{-\infty}P(x)=1[/tex]
then
[tex]\int^{\infty}_{-\infty}P(kx)=\frac{1}{k}[/tex]

when does this apply? Does it apply for all improper integrals from [tex]-\infty[/tex] to [tex]\infty[/tex] or only when the integral evaluates to 1?
The article where I read it stated it as something obvious with no explanations or conditions.
 
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Oh... I just did a simple variable substitution (u = kx) and it was obvious. Sorry!
 

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