Let $X_1,\dots,X_n$ are i.i.d random variables with geometric distribution, and the successful probability is $p$ for each $X_i$.
So for any $X_i$, the probability mass function is $\Pr(X_i=k)=(1-p)^{k-1}p$
Define a list of indicator variables $Y_1,\dots,Y_n$, which for an integer $b>0$, $ Y_i=\left\{ \begin{aligned} 1 && X_i \le b\\ 0 && X_i >b \end{aligned} \right. $
So my question is what is the distribution of $\sum\limits_{i=1}^n Y_i?$