$\displaystyle p_t (x,A) = \sum_{y=0}^x \dbinom{x}{y} (e^{-\mu t})^x (1-e^{-\mu t})^{x-y} 1_A(y)$ for $\displaystyle x \in \mathbb{N}_0, \ \mu >0 \ A \in \mathcal{B}$

Show this satisfies the Chapman-Kolmogorov equation.