Discuss the below:
Q1. Assume that the number of uninspected cars caught at a state police checkpoint is Poisson distributed with average 2.1 per hour. (a) What is the average number of cars caught in t hours? (b) What are P(no cars caught in 14 hours? (c) P(at least 3 in 1.5 hours); (d) P(at least 1 car caught within 10 minutes of setting up the checkpoint)?
Q2 a. Assume that batteries last for a time that is exponentially distributed with average 2 Months. If a transmitter needs one battery at a time and 4 (including the original) are taken on a expedition, what are (a)
P(Transmitter last at least 11 Months)?
Q3. Louise sells encyclopedias door to door. She stops for the day after 4 sales. Assume that the time between sales is exponentially distributed. (a) If she can expect to work for 7 hours to make the 4 sales, what is the parameter / ? What is the probability that she will stop (b) before 6 hours; (c) after 9 hours?
Q4. Suppose that customers enter a store according to a Poisson stream with average 40.7 for a whole day. Suppose that 2 out of5 customers result in a sale. What is the distribution for the number of sales in half a day.