Question

Of students at a particular university:

• 20% are freshmen
• 22% are sophomores
• 23% are juniors
• 28% are seniors
• 7% are graduate students.

Additionally, 60% of students are female. You may assume that being female is independent of the above classifications.

A student will be selected at random and the variable CODE is defined based on the classification of the selected student:

• If freshmen, CODE = 1
• If sophomore, CODE = 2
• If junior, CODE = 3
• If senior, CODE = 4
• If graduate student, CODE = 5

What is the expected value of CODE?

Answer 1

Answer:

Given Data

Of students at a particular university:

• 20% are freshmen
• 22% are sophomores
• 23% are juniors
• 28% are seniors
• 7% are graduate students.

Additionally, 60% of students are fem

A student will be selected at random and

the variable CODE is defined based on the classification of the selected student:

• If freshmen, CODE = 1
• If sophomore, CODE = 2
• If junior, CODE = 3
• If senior, CODE = 4
• If graduate student, CODE = 5

Let us construct the table of probabiity distribution

Code	Probability
1	0.2
2	0.22
3	0.23
4	0.28
5	0.07

We know that

E(X) = .P(X)

Thus we get

E(CODE) = 1 * 0.2 + 2 * 0.22 + 3 * 0.23 + 4 * 0.28 + 5 * 0.07 = 2.8

Expected value of CODE = 2.8