Assume the the time required to download a file from the Internet is exponentially distrubuted with mean equal to 4 minutes. What is the probablity that a download will require at least 2 but not more then 4 minutes. (to five decimal places)?
Assume the the time required to download a file from the Internet is exponentially distrubuted with mean equal to 4 minutes. What is the probablity that a download will require at least 2 but not more then 4 minutes. (to five decimal places)?
The pdf of the exponential distribution is:Originally Posted by sweettea331
$\displaystyle p(x)=\left \{ \begin{array}{cc}\frac{1}{\bar x}e^{-x/\bar x}& x \ge 0\\0&x<0 \end{array}\right$.
Here $\displaystyle \bar x=4$, and the required probability is:
$\displaystyle P(2<x<4)=\int ^4 _2 p(x) dx=\int ^4 _2 \frac{e^{-x/4}}{4} dx$
which you should be able to evaluate.
RonL