- #1
crbazevedo
- 7
- 0
Hello everyone,
I'm new to this forum and I'm glad to have found such a high quality resource where we can have such valuable guidance and discussions.
I've read somewhere that the variance of [tex]p(x) = {\frac{1}{n}}\sum_{i=1}^{n}\delta(x-x_i) \forall x \in \Re[\tex],
in which [tex]D_n = \left\{x_1, \cdots, x_n\right\}[\tex] independent realizations of a continuous random variable [tex]X[\tex], and [tex]\delta[\tex] is the dirac delta function, is infinite, irrespective to [tex]n[\tex] and [tex]D_n[\tex].
My questions are straightforward:
1) Why is that (my guess that the integral involved in the variance calculation does not converge)?;
2) What does it mean to have infinite variance in practical terms?;
3) Any practical examples where a distribution with infinite variance would be useful?;
Please note that I don't have a strong background in statistics.
Any help will be much appreciated.
Cheers,
Carlos
I'm new to this forum and I'm glad to have found such a high quality resource where we can have such valuable guidance and discussions.
I've read somewhere that the variance of [tex]p(x) = {\frac{1}{n}}\sum_{i=1}^{n}\delta(x-x_i) \forall x \in \Re[\tex],
in which [tex]D_n = \left\{x_1, \cdots, x_n\right\}[\tex] independent realizations of a continuous random variable [tex]X[\tex], and [tex]\delta[\tex] is the dirac delta function, is infinite, irrespective to [tex]n[\tex] and [tex]D_n[\tex].
My questions are straightforward:
1) Why is that (my guess that the integral involved in the variance calculation does not converge)?;
2) What does it mean to have infinite variance in practical terms?;
3) Any practical examples where a distribution with infinite variance would be useful?;
Please note that I don't have a strong background in statistics.
Any help will be much appreciated.
Cheers,
Carlos
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