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8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.

8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.
Transcribed Image Text:8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.
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