# Probability of rainfall exceeding mean value

Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.

a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)

b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)

c. What is the probability that it is less than the mean value by more than one standard deviation? (0)

My try: I got part a) and I am getting 0.668 for b) but answer should be 0.0498 and same for par c). I got 0.236 for part c but it should be 0 according the solution in the back.

Can someone help me with part b and c.

• For an exponential with mean $\mu$, the variance is $\mu^2$, so the standard deviation is $\mu$. So c) asks for the probability a rain event has length $\lt \mu-\mu$, that is, $\lt 0$. This cannot happen. – André Nicolas Mar 3 '16 at 22:28
• Ohh I get it. I was calculating P( X < μ+σ) . – max Mar 3 '16 at 22:31

## 1 Answer

For an exponential with mean $\mu$, the variance is $\mu^2$, so the standard deviation is $\mu$.

b) We want the probability that the duration is $\gt 2.725+2(2.725)$. I expect you can solve this using techniques that you used in a).

c) This asks for the probability a rain event has length $\lt \mu-\mu$, that is, $\lt 0$. That cannot happen.