Two independent Poisson variables X∼Poisson(2)X \sim Poisson(2)X∼Poisson(2) and Y∼Poisson(3)Y \sim Poisson(3)Y∼Poisson(3) are summed to form Z=X+YZ = X + YZ=X+Y. What is P(Z=0)P(Z=0)P(Z=0)?
e−5e^{-5}e−5
e−2+e−3e^{-2} + e^{-3}e−2+e−3
e−6e^{-6}e−6
1−e−51 - e^{-5}1−e−5