Assignment:
1. A system is subject to shocks that occur according to a Poisson process with parameter λ. Assume that the system stops working after an integer number k of consecutive shocks. Determine the PDF of the time T at which the system breaks down.
2. A system is subject to shocks that occur in time according to the arrivals of a Poisson process with parameter λ. The system survives each shock with probability α, independently of how many shocks it has already undergone. Conversely, each shock may break down the system with probability 1 - α. Find the probability that the system is still running at time t.