1. ## exponential distribution

Hi can anybody help me with exponential distribution?

The speed of wind can be modelled with an exponential distribution with a mean of 40 miles per hour.
At a random location what is the probability that wind speed is less than 25 miles per hour?
What is the probability at a random location wind speed will exceed 100 miles an hour?

Now i know that this can be modelled as lamda e^(-lamda x)
and i also know that in that equation that lamda can be replaced by 1/40 (i think!) But i'm not sure how to work out the question. Can anybody give me a hand?

2. Hi
Originally Posted by studentsteve1202
Now i know that this can be modelled as lamda e^(-lamda x)
There is just a $\displaystyle \lambda$ missing : $\displaystyle f_X(x)=\lambda\exp(-\lambda x)$ with $\displaystyle x\geq 0$.
and i also know that in that equation that lamda can be replaced by 1/40
Yes
But i'm not sure how to work out the question. Can anybody give me a hand?
Denote $\displaystyle V$ the random variable associated to the wind speed

The probability that the wind speed is less than $\displaystyle V_0$ is given by
$\displaystyle P(V\leq V_0)=\int_0^{V_0}\lambda\exp(-\lambda x)\mathrm{d}x$

As the wind speed is either greater than $\displaystyle V_0$, either less than $\displaystyle V_0$, $\displaystyle P(V\geq V_0)=1-P(V\leq V_0)$.

Hope that helps.