Customers arrive at a service facility according to a Poisson process of rate 5 /hour Let...

Customers arrive at a service facility according to a Poisson process of rate 5 /hour Let N(t) be the number of customers that have arrived up to time t hours).

What is the probability that there is at least 2 customer walked in 30 mins?

b.If there was no customer in the first30 minutes, what is the probability that you have to wait in total of more than 1 hours for the 1 st customer to show up?

c.For an y random customer, if there is 50% chance the customer is female, what is the expected waiting time until the

5th female customer comes in?

Solutions

Expert Solution

The number of arrivals at in time is a random variable can be modeled by Poisson distribution.

The Poisson PMF is

. Here is the Poisson parameter - the average number of events in unit time.

a) The probability,

b) The time till the first arrival is exponentially distributed with . The probability that you have to wait in total of more than 1 hours for the 1st customer to show up (wait more than 1/2 hours) is

c) The waiting time till the th female customer has Gamma distribution. . Here . The expected value of (Gamma distribution) is

orchestra answered 1 year ago

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