Question

The lag time between truck arrivals at the workshop is a continuous random variable. The probability of time between arrivals is expressed as a probability density function, namely: f(t) = 5e‐⁵t Set for t>0 f(t) = 0 for t<0 Where t is time (hours) a. Determine the average time between arrivals of trucks (hours) b. Determine the standard deviation of the time between arrivals (hours)

Answer 1

for Exponential distribution:

$f(t) = \lambda e^{-\lambda t}$

where $\lambda=1/\mu$ is rate parameter

a.

we have:

$\lambda=5$

then average time between arrivals:

$\mu=1/\lambda=1/5$ hour = $12$ min

b.

 standard deviation of the time between arrivals:

$\sigma =\mu=1/\lambda=1/5$ hour = $12$ min