Question

Times between bus arrivals are exponentially distributed with mean = 15 minutes (lambda = 1/15). you have been waiting for 10 minutes. what is the expected time until the bus arrives?

Answer 1

Exponentially distributed bus arrival times have a mean of 15 minutes (lambda = 1/15). It's been ten minutes since you last checked. The bus shouldn't show up for another fifteen minutes.

The bus arrival time is exponentially distributed, with a mean of 15 minutes. Let X be the random variable that captures the duration of the bus wait. The following is the probability distribution of X:

P(X = x) = $\lambda e^{-\lambda x}$

We have

$\lambda = \frac{1}{15}$

Ten minutes have already passed while you waited. The estimated time of arrival for the bus will always be 15 minutes since exponential distributions are memoryless, regardless of how long people wait.

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