exponential distribution

**studentsteve1202** · May 2nd 2008, 12:00 PM

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?

**flyingsquirrel** · May 2nd 2008, 12:10 PM

Hi

Originally Posted by studentsteve1202

Now i know that this can be modelled as lamda e^(-lamda x)

There is just a $\lambda$ missing : $f_X(x)=\lambda\exp(-\lambda x)$ with $x\geq 0$ .

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 $V$ the random variable associated to the wind speed

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

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

Hope that helps.

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