A random variable is Poisson distributed with = 1.5 occurrences per hour. For the corresponding exponential

Question:

A random variable is Poisson distributed with λ = 1.5 occurrences per hour. For the corresponding exponential distribution, and x = hours until the next occurrence, identify the mean of x and determine the following:
a. P(x ≥ 0.5)
b. P(x ≥ 1.0)
c. P(x ≥ 1.5)
d. P(x ≥ 2.0)