Question

1. Hank is an intelligent student and usually makes good grades, provided that he can review the course material the night before the test. For tomorrow's test, Hank is faced with a small problem: His fraternity brothers are having an all-night party in which he would like to participate. Hank has three options: a1 - party all night: 2-divide the night equally between studying and partying: 3 - study all night. Tomorrow's exam can be easy (s1), moderate (S2) or tough (53), depending on the professor's unpredictable mood. Hank anticipates the following scores:

S1 S2 S3
a1 85 60 40
a2 92 85 81
a3 100 88 82

(a) Recommend a course of action for Hank based on each of the four criteria of decisions under uncertainty.
(b) Suppose that Hank is more interested in the letter grade he will get. The dividing scores for the passing letter grades A to Dare 90, 80, 70 and 60, respectively. What should the decision/s be?

Answer 1

Answer and Step-by-step explanation:

The answer is attached below

Answer 2

The expected pay-off for a₃ is maximum. Then the decision a₃ (study all night) is considered.

What are statistics?

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, summarise the data.

Hank is an intelligent student and usually makes good grades, provided that he can review the course material the night before the test.

For tomorrow's test, Hank is faced with a small problem: His fraternity brothers are having an all-night party in which he would like to participate.

Hank has three options:

a₁ - party all night

a₂ - divide the night equally between studying and partying

a₃ - study all night

Tomorrow's exam can be easy (S₁), moderate (S₂) or tough (S₃), depending on the professor's unpredictable mood. Hank anticipates the following scores:

             S₁               S₂             S₃

a₁          85              60             40

a₂         92              85             81

a₃        100              88             82

Decision under uncertainty

1.  For maximum criterion when the exam is tough.

a₁  = 40, a₂ = 81, and a₃ = 82

Since 82 is the maximum out of the minimum. Then the optional action is a₃ (study all night).

2.  For maximum criterion when the exam is easy.

a₁  = 85, a₂ = 92, and a₃ = 100

Since 82 is the maximum out of the maximum. Then the optional action is a₃ (study all night).

3.  Regret criterion

First, find the regret matrix.

             S₁               S₂             S₃         Max. regret

a₁          15              28             42                 42

a₂          8                3                1                   8

a₃          0                0               0                   0

From the maximum regret column, we find that the regret corresponding to the course of action is a₃ is minimum. Therefore, decision a₃ (study all night) will be considered.

4.  Laplace criterion

The probability of occurrence is 1/3.

Therefore, the expected pay-off for each decision will be

E(a₁) = 61.67, E(a₂) = 86, and E(a₃) = 90

Therefore, the expected pay-off for a₃ is maximum.

Thus, decision a₃ (study all night) is considered.

More about the statistics link is given below.

https://brainly.com/question/10951564