Problem 7) UIC students were given three choices of pizza toppings and asked to
ID: 3062381 • Letter: P
Question
Problem 7) UIC students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results.
Toppings
Freshmen
Sophomore
Junior
Senior
Totals
Cheese
14
11
28
29
82
Meat
23
29
11
14
77
Veggie
11
14
23
29
77
Totals
48
54
62
72
236
(5 points) If the variable Y is the number of years of a student at school, construct the probability distribution for variable Y.
(10 points) What is the Expected number of years at the University for a student in this sample?
(10 points) Create the Joint Distribution table for variables X and Y
Toppings
Freshmen
Sophomore
Junior
Senior
Totals
Cheese
14
11
28
29
82
Meat
23
29
11
14
77
Veggie
11
14
23
29
77
Totals
48
54
62
72
236
Explanation / Answer
Here for freshmen ; X = 1
For Sophomore , X =2
for Junior , X = 3
for Senior , X = 4
f(x) = 48/236 = 0.2034 ; X = 1
= 54/236 = 0.2288 ; X = 2
= 62/236 = 0.2627 ; X = 3
= 72/236 = 0.3051 ; X = 4
(b) Here
E(X) = 1 * 0.2034 + 2 * 0.2288 + 3 * 0.2627 + 4 * 0.3051 = 2.6695
(c) Here is the joint disribution table is given below
Toppings Freshmen Sophomore Junior Senior Totals Cheese 0.0593 0.0466 0.1186 0.1229 0.3475 Meat 0.0975 0.1229 0.0466 0.0593 0.3263 Veggie 0.0466 0.0593 0.0975 0.1229 0.3263 Totals 0.2034 0.2288 0.2627 0.3051 1.0000