Calculating lambda in statistics
I am trying to figure out how to find lambda for a question:
Compute the probability of taking at least 7 minutes to receive a call.
The exponential mean is 5.
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$\begingroup$The density function for exponential distribution with mean 5 is: $f(x)=1/5*e^{-5/x}$.
Then if you want to find the probability of receiving the call after waiting at least 7 minutes, you just integral the density function on the interval of [7,$\infty$].
lambda is just the inverse of your mean, in is case, 1/5.
$\endgroup$ $\begingroup$Ordinarily, we say that the random variable $X$ has exponential distribution with parameter $\lambda$ if $X$ has density function $\lambda e^{-\lambda x}$ (for positive $x$).
The mean of such a random variable $X$ is equal to $\frac{1}{\lambda}$.
It follows that if you are told that the mean is $5$ minutes, then $\frac{1}{\lambda}=5$, and therefore $\lambda=\frac{1}{5}$.
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