Could you explain these two questions

In a homogeneous arrival-counting Poisson process (Nt) with rate ), a counting device misses counting an event with probability p, independent of everything else. Prove that the actually counted process (Zt) is a homogeneous arrival-counting Poisson process with rate A(1 - p). Let X1, X2, ... be independent discrete random variables such that P(X = k) = cx (1 -p)k k k 2 1, 0