Consider an Exponential random variable X with parameter > 0. Let Y = [X], which means we get Y by rounding X down to

Consider an Exponential random variable X with parameter λ > 0. Let Y = [X], which means we get Y by rounding X down to the barest integer (in particular, Y itself is a discrete random variable, because Y is always an integer). For example, if X = 7.2, then Y = 7. If X = 12.9999, then Y = 12. If X = 5.01, then Y = 5, etc.
So the mass of Y is exactly
PY(y) = P(Y = y) = P(y ≤ X ≤ y + 1).
a. Find an expression for the mass of Y. (Your expression will have A in it;
i.e., just integrate to find the value of P(y ≤ X ≤ y + 1), and then simplify.)
b. Do you recognize the mass of Y? (Yes, you should!) What type of random variable is Y? What are the parameters of Y?