Distribution Function from Density Function I'm guessing there was an error in a Probability and Statistics exam I have recently taken.
Let $X$ be a random continuous variable and $f$ a function defined as follows:
$
f(x)=\left\{\begin{matrix}
Ce^{-2x}  & , x < 0\\ 
0 & x \geq  0
\end{matrix}\right.
$
The question was to determine the constant $C$ so that the function $f$ is a density function, and then to calculate the distribution function.
My thinking was that the integral when $x < 0$  (i.e. over $]-∞, 0[$) cannot be calculated ($=+∞$), and this is the interval over which the function $f(x)$ must be integrated.
Am I correct or my thinking is wrong?

You are right.
Very likely, they have switched the conditions. What they probably meant was:
$$
f(x)=\left\{\begin{matrix}
0 & x <  0\\
Ce^{-2x}  & , x \geq 0
\end{matrix}\right.
$$
