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Suppose occurrences of sales on a small​ company's website are well modeled by a Poisson model

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Asked: Jul 13,2019 In: Probability
3 Answers
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Asked: Jul 13,2019 In: Probability

Suppose occurrences of sales on a small​ company's website are well modeled by a Poisson model

Suppose occurrences of sales on a small​ company's website are well modeled by a Poisson model with lambda  = 2/hour
.
​a) If a sale just​ occurred, what is the expected waiting time until the next​ sale?
​b) What is the probability that the next sale will happen in the next 18 ​minutes?


Poisson distribution
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tutor Added an answer on Jul 13,2019

The expected waiting time until the next sale is  = 1/2 

Probability that the sale occurs in the next 18 minutes. 

If a discrete random variable can be modeled by a Poisson model with rate lambda
​, then the times between those events can be modeled by an exponential model with the same parameter lambda
.
To find the​ probability, use the cumulative distribution function of the exponential distribution given below.

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