# The Exponential Distribution

• April 29th 2009, 01:21 PM
chella182
[SOLVED] The Exponential Distribution
The question goes as follows...

Annual wind speed maxia for various hurricane-prone locations in the American Deep South can be modelled with an exponential distribution with mean 58 miles per hour.

a) Find the probability that, for a randomly chosen location in the Deep South, the annual maximum wind speed is less than 30 miles per hour.

b) Find the probability that, for one of these locations, the annual maximum wind speed will exceed that observed for New Orleans during Hurricane Katrina of 181 miles per hour.
For the first part I got an answer of 1 when I initally tried it, which is obviously wrong. Thanks in advance for any help :)
• April 29th 2009, 07:50 PM
mr fantastic
Quote:

Originally Posted by chella182
The question goes as follows...

Annual wind speed maxia for various hurricane-prone locations in the American Deep South can be modelled with an exponential distribution with mean 58 miles per hour.

a) Find the probability that, for a randomly chosen location in the Deep South, the annual maximum wind speed is less than 30 miles per hour.

b) Find the probability that, for one of these locations, the annual maximum wind speed will exceed that observed for New Orleans during Hurricane Katrina of 181 miles per hour.

For the first part I got an answer of 1 when I initally tried it, which is obviously wrong. Thanks in advance for any help :)

Let the pdf be f(x).

a) $\Pr(X < 30) = \int_0^{30} f(x) \, dx$.

b) $\Pr(X > 181) = \int_{181}^{+\infty} f(x) \, dx$.
• April 30th 2009, 06:09 AM
chella182
Okay, this is sorted now - one of my friends in the year above me pointed out my silly mistake :p