Question

Question 1: A drive-in movie theatre charges viewers by the carload but keeps careful records of the number of people in each car. The probability distribution for the number of people in each car entering the drive-in is given in the table.

x = (px)

1= 0.02

2= 0.30

3=0.10

4= 0.30

5= 0.20

6=0.08

a. Suppose two cars entering the drive-in are selected at random. Find the exact probability distribution for the maximum number of people in either one of the cars, M. (Show all your work in order to get full marks, i.e., show: 1. the total number of samples of two cars, 2. the list all the possible samples of two cars, the value of max, and the corresponding probability. 3. the exact distribution for the maximum number of people in either one of the cars).

b. Find the mean, variance, and standard deviation of M.

Answer 1

Answer:

Sample	Max	Probability
(1,1)	1	0.02^2 = 0.0004
(1,2)	2	0.02*0.30
(1,3)	3	0.02*0.1
(1,4)	4	0.02*0.30
(1,5)	5	0.02*0.20
(1,6)	6	0.02*0.08
(2,1)	2	0.30*0.02
(2,2)	2	0.30*0.30
(2,3)	3	0.30*0.10
(2,4)	4	0.30*0.30
(2,5)	5	0.30*0.20
(2,6)	6	0.30*0.08
(3,1)	3	0.10*0.02
(3,2)	3	0.10*0.30
(3,3)	3	0.10*0.10
(3,4)	4	0.10*0.30
(3,5)	5	0.10*0.20
(3,6)	6	0.10*0.08
(4,1)	4	0.30*0.02
(4,2)	4	0.30*0.30
(4,3)	4	0.30*0.10
(4,4)	4	0.30*0.30
(4,5)	5	0.30*0.20
(4,6)	6	0.30*0.08
(5,1)	5	0.20*0.02
(5,2)	5	0.20*0.30
(5,3)	5	0.20*0.10
(5,4)	5	0.20*0.30
(5,5)	5	0.20*0.20
(5,6)	6	0.20*0.08
(6,1)	6	0.08*0.02
(6,2)	6	0.08*0.30
(6,3)	6	0.08*0.10
(6,4)	6	0.08*0.30
(6,5)	6	0.08*0.20
(6,6)	6	0.08*0.08

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