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Events occur according to a Poisson process with rate \lambda - 2 per hour. a. What is the...

Question:

Events occur according to a Poisson process with rate {eq}\lambda {/eq} - 2 per hour.

a. What is the probability that no event occurs between between 8 pm and 9 pm?

b. Starting at noon, what is the expected time at which the fourth event occurs?

c. What is the probability that two or more events occur between 6 pm and 8 pm?

Poisson Process

It has a Poisson number of successes over time. The time between successes are Exponentially distributed with the same {eq}\lambda. {/eq} If you change the amount of time, but are still looking at number of successes, you still have a Poisson, but you have to adjust {eq}\lambda {/eq} based on the new time frame.

Lastly, the pmf of a Poisson is {eq}p(x) = e^{-\lambda} \lambda^x/x! \quad x = 0, 1, ... {/eq}

Answer and Explanation: 1

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Answers:

A) .1353

B) 2 hours

C) .9084

Work:

Let X be the number of events in a 1 hour period. {eq}X \sim Poi(\lambda = 2). {/eq}

a) P(X = 0) =...

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Poisson Distribution: Definition, Formula & Examples

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Chapter 2 / Lesson 24
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Poisson distribution is a discrete distribution used to determine the probability of the number of times an event is likely to occur in a certain period. Explore the definition, formula, conditions, and examples of Poisson distribution.


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