The time between customers in a shop has an exponential distribution with mean of 2 minutes. Five minutes have passed since the last customer. What is the conditional probability that the next customer will arrive within 3 minutes?
It says the answer is 0.777, but I don't know how they got it.
It says the answer is 0.777, but I don't know how they got it.
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A feature of the exponential distribution is that what has happened in the past does not matter. This means you just work out the probability of a customer arriving in the next 3 minutes.
P(x < 3) = 1 - e^(-3/2) = 0.777 (3 d.p.)
P(x < 3) = 1 - e^(-3/2) = 0.777 (3 d.p.)