Probability of No Events in First Two Hours for Poisson Process with Rate 2

[Quincy]

Homework Statement

Consider a Poisson process for which events occur at a rate of 2 per hour.
(a) Give the probability that the time until the first event occurs exceeds 2 hours. Use an exponential distribution to find the probability.

Homework Equations

The Attempt at a Solution

$$\lambda$$ = 1/2

pdf = (1/2)e^-x/2, x >= 0

The probability that the time until the first event occurs exceeds two hours, is equal to the probability that 0 events occur in the first two hours.
I have the pdf, but I'm not sure how to use it to find the probability.

 

[LCKurtz]

P(x > 2) = 1 - p(x=1) - p(x=2)