In a factory, a certain machine operates for a period which is exponentially distributed with parameter λ. Then it breaks down and will be in repair shop for a period, which is also exponentially...

In a factory, a certain machine operates for a period which is exponentially distributed with parameter λ. Then it breaks down and will be in repair shop for a period, which is also exponentially distributed with mean 1/λ. The operating and the repair times are independent. For this machine, we say that a change of “state” occurs each time that it breaks down, or each time that it is fixed. In a time interval of length t, find the probability mass function of the number of times a change of state occurs.