Each time the frozen yogurt machine at the mall breaks down, it is replaced by a new one of the same type. (a) What is the limiting age distribution for the machine in use if the lifetime of a machine...

Each time the frozen yogurt machine at the mall breaks down, it is replaced by a new one of the same type. (a) What is the limiting age distribution for the machine in use if the lifetime of a machine has a gamma(2,λ) distribution, i.e., the sum of two exponentials with mean 1/λ. (b) Find the answer to (a) by thinking about a rate one Poisson process in which arrivals are alternately colored red and blue.