The density function of the time Z in minutes between calls to an electri- cal s

Question

The density function of the time Z in minutes between calls to an electri-
cal supply store is given by

f(z)= (1/10)e^(-z/10) , 0 < z < 8 f(z)= 0 , otherwise.
(a)What is the mean time between calls?
(b) What is the variance in the time between calls?
(c) What is the probability that the time between calls exceeds the mean? The density function of the time Z in minutes between calls to an electri-
cal supply store is given by

f(z)= (1/10)e^(-z/10) , 0 < z < 8 f(z)= 0 , otherwise.
(a)What is the mean time between calls?
(b) What is the variance in the time between calls?
(c) What is the probability that the time between calls exceeds the mean?

Explanation / Answer

nevermind one of the previous answers that I gave. Will use cumulative function for exponential distribution, as this is an exponential distribution. I've not touched anything aside from normal, t, and F distributions in a very long time. Anything that calls for a "between", "before", or "after" a certain time probability is calculated with the cumulative distribution equation. in an exponential distribution we have p=lambda*e^(-lambda*x) in this case, lamda=1/10, x=z a. mean is 1/lambda, or 10 b. variance is 1/(lambda)^2=100 c. This calls for the cumulative distribution function: 1-e^(-lambda*x) Since we're calculating the probability of exceeding the mean, we have 1-(1-e^(-lambda*x)) which is equal to: 0.3679

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