I need help solving this problem. Please help me by answering and showing explanations.

Problem 4. (25 points). Engineer Nick's is often the victim of litigation. Lawsuits come in at random intervals, and can be modeled by a Poisson process with a mean of 2 per month. (a (5) What is the expected time until the next lawsuit comes in? (c (d ) (b) (5) What is the median time until the next lawsuit comes in? ) (5) What is the probability that there are no lawsuits during the 3 months you work during the summer? ) (5) After the next two lawsuits, the rm will have to close. Write down the PDF for the time until this happens. (e) (5) What are the mean and standard deviation of the time before the rm closes