Suppose X has an exponential distribution with A = 2.

Determine the following:

(a) PX0)

(b) P(X2)

(c) P1)

(d) P(1 < <2)

(e) Find the value of x such that P(X 20)

(c) P(X <30)

(d) Find the value of x such that P(X

(a) What is the probability that there are no calls within a 30-minute interval?

(b) What is the probability that at least one call arrives within a 10-minute interval?

(c) What is the probability that the first call arrives within 5 and 10 minutes after opening?

(d) Determine the length of an interval of time such that the probability of at least one call in the interval is 0.90.