4. Assume you operate a buisness and you are waiting for the first customer to a

Question

4. Assume you operate a buisness and you are waiting for the first customer to arrive at the store. It is believed that the wait time follows an Exponential distribution with parameter A minutes a What is the probability that you wait for more than 3 minutes? P()6915 1 ·6873 b. What is the expected time (in minutes) that you wait for the first customer to arrive? E(X): 8 minutes CNow say you have almady waited for 2hintes Wha is the -of·ait at last an additional(3)ninates for a customer to arrive? A'/g you will have to 6813 d. You are to wait for 10 customers to arrive. Aseume the customers are independent of one another How long do you expect to wait to complete this task (obeerve 10 customers)? How much do you expect your wait time to vary around the expected time? iv

Explanation / Answer

d)
T = X1 +X2+ ..X10
T follow erlang distribution

mean = 10*8 = 80 min
variance = 10*8*8 = 640 min^2
sd = sqrt(640) = 25.29822 min

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