How to calculate expected value for piecewise constant distribution function? The distribution function of a discrete random variable X is given
$F_X(x)=\begin{cases} 0, &x<1\\ \frac{5}{13},& 1\leq x< 2  \\ \frac{10}{13}, & 2\leq x<3 \\ \frac{11}{13}, & 3\leq x<4 \\ 1, & 4\leq x   \end{cases} $
$A=(X=2)\cup  (X=4)$
Calculate: $P(A)$ and $E(X)$
I was thinking to solve $P(A)$ with formula: $P(a)=\begin{pmatrix} n \\ a  \end{pmatrix} p^a (1-p)^{n-a} $, but I dont $p$ and $n$. Which formula I should use?

the random variable $X$ can take four values, which are exactly the points of discontinuity of $F_X$:
$$
\mathbb P (X=1)= \frac 5 {13}, \quad \mathbb P (X=2)=\frac {10} {13}- \frac 5 {13}, \quad
\mathbb P (X=3)=\frac {11} {13} -\frac {10} {13}, \quad \mathbb P (X=4)=1- \frac {11} {13}. \quad
$$
Therefore
$$
\mathbb P(A)=\mathbb P(X=2)+\mathbb P(X=4) = \frac 7 {13},
$$
and 
$$
\mathbb E [X]= 1 \cdot \frac {5}{13}+2 \cdot \frac {5}{13}+3 \cdot \frac {1}{13}+4 \cdot \frac {2}{13}=2.
$$
