19
votes
18answers
2k views

How to understand why $x^0 = 1$, where $x$ is any real number?

Alright, so the idea of an exponent, $x$, is that you are multiplying its base by itself $x$ number of times. With base $5$ and $x=3$, we have that $5^3$ = $5 \cdot 5 \cdot 5$ I understand that the ...
0
votes
0answers
31 views

Why does this general expression covering all f(u) reduce to a specific f(u)?

The following expression is sometimes encountered in statistical engineering and biology: $$r(u)=\frac{f(u)}{1-F(u)}$$ where $F(u)$ is the cumulative distribution function corresponding to the ...