# Law of the Unconscious Statistician - history of the term?

The "Law of the Unconscious Statistician" states that, for a random variable $X$ with density $f_X(x)$ and a function of it $h(X)$ we have that

$$E[h(X)] = \int_{-\infty}^{\infty} f_X(x)h(x) dx$$

In words, we do not need to obtain the distribution and density of $Z=h(X)$ in order to calculate its expected value.

How this strange name for this law came about? (it does sound a little dismissive).

The wikipedia page does not discuss the issue. The Quora forum has a related thread, but no real historical answer regarding the name is given.

But apparently the nickname only took off after Ross's "Introduction to Probability Models" (1980). Proposition 4.1 of Chapter 2 has a footnote that reads:"This law got its name from "unconscious" statisticians who ave used it as if it were the definition of $E[g(X)]$". It did not go over too well, for example Berger and Casella write in Statistical Inference:"Ross 1988 refers to this as the 'law of the unconscious statistician'. We do not find this amusing". Apparently, they were not alone, Ross dropped the nickname from subsequent editions.