Mixing Poisson Random Variables 1

Assume that  \(X\), \(Y\), and \(Z\) are independent Poisson random variables, each with mean 1. Find

1. \(\mathbf{P}(X+Y = 4) \)
2. \(\mathbf{E}[(X+Y)^2]\)
3. \(\mathbf{P}(X+Y + Z= 4) \)