Let \(X\sim\text{Exponential}(\lambda)\) for some arbitrary \(\lambda>0\). Define a new random variable \(Y=\lceil X\rceil\). Recall that the ceiling function \(\lceil\cdot\rceil\) is the function that rounds a number up to the next integer. So \(\lceil0.5\rceil=1\), \(\lceil13.1\rceil=14\), and so on.

1. What is the range of \(Y\)?
2. What is the PMF of \(Y\)?
3. Does \(Y\) belong to a familiar distribution family?