Defects in an hour follows a poisson distribution

Question

Question: A high volume production process produces, on average, 3.4 defective parts per hour, and the number of defects in an hour follows a Poisson distribution. Let Xi= the number of defects produced in hour i(i= 1, 2).

a) Find Pr(X₁= k) for k= 0, ..., 20.

b) Assuming that X₁ and X₂ are independent, calculate Pr(X₁+ X₂= k) for k= 0 to 20

c) Verify numerically that Y = X1+ X2has a Poisson distribution. What are its mean and variance?