The arrival of warranty claims at an automobile dealership follow a Poisson process with a rate of 2 per day. Find the following probabilities where X = time between consecutive claims:

(a) P(X > 2 days),

(b) P(X < 1 day), and

(c) P(0.5 < X < 1.5 days). Find the values of x0 if

(d) P(X < x0) = 0.1, and

(e) P(X > x0) = 0.05.