I hope you can help me because I have no clue where to start:
Let $X$ be a discrete random variable with $ p_k=P_X[X=x_k]=p(x_k) $for all $1\le k\le N$ for $N\in \Bbb N$ and distribuition function: $$F_X:\Bbb R\rightarrow [0,1], F_x(x)=\sum_{k=1}^N p_k1_{\{x_k\le x\}}.$$ $1_A$, for $A\in \mathfrak F$, is the characteristic function also written as $\mathcal X_A$.
Now there's a uniformly distributed random variable $U$ on $[0,1]$. My task is to get the inverse:$F^{-1}_X(u):=\inf\{x\in \Bbb R|F_X(x)\ge u\}, u\in (0,1)$ of $F_X$. I also have to scrabble a map.
Edit: It is$$F_x=\begin{cases} 0, & \text{if }x<1\\ \sum_{k=1}^N p_k1_{\{x_k\le x\}}, & \text{if }x\le x_N\\ 1, & \text{if }x\ge x_N \end{cases}$$.