Expectation of a density function

Stats_Newbie

New Member
Hi guys,

I have a question about the calculation of the expectation based on a density function where the integral is NOT 1.

Is it okay to normalize such a function and how would this work. Could anybody give a simple example?

Thanks!

Dason

It doesn't really make sense to talk about expectation unless you have a probability measure. If the integral is not 1 you don't have a probability measure. What exactly are you doing?

Stats_Newbie

New Member
Yepp this was also my thought but I read the following: Let $$f(t)$$ be an function, no properties listed but I guess that $$\int \limits_0^\infty f(t) dt < \infty$$ then they define:

$$mean = \frac{\int \limits_0^\infty t f(t) dt}{\int \limits_0^\infty f(t) dt}$$

$$var = \frac{\int \limits_0^\infty (t-mean)^2 f(t) dt}{\int \limits_0^\infty f(t) dt}$$