Probability mass function from the distribution I have the following distribution function:
\begin{equation*}
      F(x) = \begin{cases}
      0, x&lt;-1 \\ 
      \frac{1}{2}, -1 \leq x &lt; \frac{1}{2} \\ 
      \frac{3}{4}, \frac{1}{2} \leq x &lt;2 \\
      1, x \geq 2
        \end{cases}
    \end{equation*}
How can i obtain the probability mass function? My attempt was to use the discontinuites and try to evaluate the probabilities, but i was no able to confirm anything. I know that the sums off all probabilities must be one.
If before -1 the distribution function equals 0 and after -1 it equals $\frac{1}{2}$, it means that there is a mass of probability $\frac{1}{2}$ in $x=-1$.
For the same reason, there is a mass of $\frac{3}{4} - \frac{1}{2} = \frac{1}{4}$ in $x=\frac{1}{2}$, and finally a mass of $1 - \frac{3}{4} = \frac{1}{4}$ in $x = 2$.
The sum of all probabilities is $\frac{1}{2} + \frac{1}{4} + \frac{1}{4} = 1$.
Take the differences from the DF, it will give you the pdf at the jump discontinuities.