Assume X1,…,X4 are IID with Xi?Po(?). Let Y=1/4(X1+…+X4). Find Pr(Y<1/2)?

Questions
1

I have no clue where to even start with this question. Can anyone help please?

2

There is a little bit of work to do before writing any Mathematica code:

  1. Note that Pr(Y<1/2) = Pr(4 Y < 2) = Pr(X1+X2+X3+X4 < 2)
  2. The sum of iid Poissons is a Poisson.