Weighted Average and Expectation in machine learning Bishop's book  defines expectation as "weighted average of a function".
$$E[f(x)] = \int f(x)p(x)\text dx$$
However, the Wikipedia page of weighted function defines a weighted average as
$$E[f(x)] = \frac{\int w(x)f(x)\text dx}{\int w(x)\text dx}$$
Why has Bishop called Expectation as weighted "average" and not just weighted sum as the denominator term is missing in definition of expectation?

When$$\int p(x)\text dx=1$$,
$$\mathbb E_p[f(X)]=\dfrac{\int f(x)p(x)\,\text dx}{\int p(x)\,\text dx}$$
The notion is rarely used in probability books, as it does not help (and further depends on the dominating measure chosen as $\text dx$).
