1. Mechanical failures occur according to the Poisson process. Failures are classied as either major or minor. Major failures occur at the rate of 1.5 I hr. Minor failures occur at the rate of 3.0 I hr. a. What is the probability that two failures occur in 1 hour? b. What is the probability that in half an hour, no major failures occur? c. What is the probability that in 2 hours, at least 2 major failures occur OR at least two minor failures occur? 2. The University Circulator arrives at your shuttle stop according to a Poisson process with parameter u. The Campus Connector, independently of the University Circulator, arrives according to a Poisson process with parameter c. If X is the number of University Circulators that arrive between 2 successive Campus Connectors, what is the distribution of X? [Express your nal answer in terms of u, c, and x. You may also use the denition of the Gamma function E to simplify your answer}