A random variable is Poisson distributed with = 0.02 occurrences per minute. For the corresponding exponential

Question:

A random variable is Poisson distributed with λ = 0.02 occurrences per minute. For the corresponding exponential distribution, and x = minutes until the next occurrence, identify the mean of x and determine the following:
a. P(x ≥ 30.0)
b. P(x ≥ 40.0)
c. P(x ≥ 50.0)
d. P(x ≥ 60.0)