A random variable is Poisson distributed with = 0.50 arrivals per minute. For the corresponding exponential

Question:

A random variable is Poisson distributed with λ = 0.50 arrivals per minute. For the corresponding exponential distribution, and x = minutes until the next arrival, identify the mean of x and determine the following:
a. P(x ≤ 0.5)
b. P(x ≤ 1.5)
c. P(x ≥ 2.5)
d. P(x ≥ 3.0)