Interpretation of a PDF squared

Asked Oct 11 '13 at 14:20

Active Oct 11 '13 at 14:20

Viewed 49 times

I have a problem where the crucial variable is the integral of the squared PDF of a random variable, i.e.

$\int f(x)^2dx$

How should I interpret this property of a distribution? If $f(x)$ is gaussian, then this is inversely proportional to the variance, $\sigma^2$, but I don't think this is generally true.

(Note that this is also equal to $\int F(x)f'(x)dx$ ).

asked Oct 11 '13 at 14:20

tom cunningham

2

$\int f(x)^2 dx$ is also $\mathbb{E}[f(x)]$ where the expectation is with respect to $X \sim f(x)$. Does this help? – Theja Tulabandhula Oct 11 '13 at 14:28
1

Related: http://stats.stackexchange.com/questions/9926 – cardinal Oct 11 '13 at 14:37
Tom, Do the comments and the link answer your question or are you looking for something further? – cardinal Oct 11 '13 at 15:14
1

Yes I think they're good, & enough to answer my question. Thanks cardinal (not sure how to mark this as answered). – tom cunningham Oct 11 '13 at 21:43

Interpretation of a PDF squared

0 Answers0