Suppose that customers arrive at a car wash according to a Poisson process with rate λ = 8 cars per hour. The time spent by each car at the car wash is a continuous random variable with probability density function f(t) = Ae^(-0.2t) for t > 0, where t is the time spent by a car in hours. Calculate the variance of the time spent by all cars in 5 hours.
Added by Michael C.
Step 1
The mean of a continuous random variable with probability density function f(t) is given by the formula: E(t) = ∫ t * f(t) dt In this case, the probability density function is f(t) = Ae^(-0.2t). So, we need to find the value of A. To find A, we use the fact Show more…
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