Computing $P(X = 0)$ for the following mixed variable (discrete and continuous)?

Question

I've been given the following distribution:

$F_X(x) = \frac14 e^x $ if $x < 0$ and $ 1 - \frac14 e^{-x} $ if $x \geq 0$

I have not had any teaching on mixed variables as of yet. The question asks me to compute $P(X = 0)$. How do I go about doing this? I was thinking of doing something like $F_X(0) = P(X < 0) + P(X = 0) = F_X(0^-) + P(X=0)$ but I'm not sure what the LHS should equal: $\frac 14$ or $\frac 34$.

Thanks!

Answer 1

To calculate $P(X=0)$ simply evaluate the "jump" you have in $F_X(0)$ that is $3/4-1/4=1/2$