(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The mean of a function is as follows:

$${1 \over {a - b}}\int_b^a {f(x)\,dx} $$

So why is the mean of the PDF as follows:

$$\int_{ - \infty }^\infty {xf(x)\,dx} $$

I thought it would have been this way:

$$\lim \,b \to - \infty \,{1 \over { - b}}\int_b^0 {f(x)\,dx\,} + \,\,\lim \,a \to \infty {1 \over a}\int_0^a {f(x)\,dx = 0 + 0 = 0} $$

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: The mean of the Probability Density Function

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