I have another problem in a statistics past paper that goes as follows:
Let $X$ be a continuous random variable, taking values in the range $[0,1]$ with pdf given up to proportionality by $f(x) \sim x^4$, $0 \le x \le 1$. What is the value of $E(X)$?
Normally $E(X)$ should be $$\int_0^1 xf(x) ~dx,$$ right? In which case $E(X)$ would be $1/6$. But for some reason that's not the answer in the marking scheme. Does the keyword "proportionality" have anything to do with it? If so, what?