Ch. 20

___________ states that the mean outcome in many repetitions gets close to the expected value.

Law of Large Numbers

On a multiple-choice test, a student has four possible choices for each question. The student receives 1 point for a correct answer and loses ¼ point for an incorrect answer. If the student has no idea of the correct answer for a particular question and merely guesses, what is the student's expected gain or loss on the question?

0.0625

The distribution of grades (letter grade and GPA numerical equivalent value) in a large statistics course is as follows: A (4.0) 0.2; B (3.0) 0.3; C (2.0) 0.3; D (1.0) 0.1; F (0.0) ?? What is the probability of getting an F?

0.1

The distribution of grades (letter grade and GPA numerical equivalent value) in a large statistics course is as follows: A (4.0) 0.2; B (3.0) 0.3; C (2.0) 0.3; D (1.0) 0.1; F (0.0) ?? What is the expected value for GPA?

2.4

Suppose you were using an eight-sided number die that was rigged to have one side occur more than the others (not equally likely). The probability model of the trick die is: 1 - 0.5; 2 - 0.2; 3 - 0.05; 4 - 0.05; 5 - 0.05; 6 - 0.05; 7 - 0.05; 8 - 0.05

2.55

Suppose you were using an eight-sided number die that was rigged to have one side occur more than the others (not equally likely). The probability model of the trick die is: 1 - 0.5; 2 - 0.2; 3 - 0.05; 4 - 0.05; 5 - 0.05; 6 - 0.05; 7 - 0.05; 8 - 0.05 What is the expected value?

2.55

The expected value of a six-sided fair die (with all outcomes equally likely)

3.5

The expected value is

The average of all possible outcomes The sum of the products of the numerical outcomes and their respective probabilities

If you do not know the outcome probabilities, you can estimate the expected value by:

Using the Law of Large Numbers Using simulation

On a multiple-choice test, a student has four possible choices for each question. The student receives 1 point for a correct answer and loses ¼ point for an incorrect answer. If the student has no idea of the correct answer for a particular question and merely guesses, what is p(getting the correct answer) and p(choosing incorrectly)?

b. p(correct) = 0.25; p(incorrect) = 0.75