Chapter 14, Problem 12E

a)

To determine

To check whether probability assignments are legitimate.

Answer to Problem 12E

Not legitimate.

Explanation of Solution

Given:

  

The conditions for probability distribution are:

1. Each of the probability lies between 0 and 1 inclusively.
2. The sum of the all probabilities should be 1.

This is not a legitimate assignment because although each outcome has probability between 0 and 1 inclusive, the sum of the probabilities is less than 1.

b)

To determine

To check whether probability assignments are legitimate.

Answer to Problem 12E

Not legitimate.

Explanation of Solution

Given:

  

The conditions for probability distribution are:

1. Each of the probability lies between 0 and 1 inclusively.
2. The sum of the all probabilities should be 1.

This is not a legitimate probability assignment because although each outcome has a probability between 0 and 1 inclusive, the sum of the probabilities is greater than 1.

c)

To determine

To check whether probability assignments are legitimate.

Answer to Problem 12E

Legitimate.

Explanation of Solution

Given:

  

The conditions for probability distribution are:

1. Each of the probability lies between 0 and 1 inclusively.
2. The sum of the all probabilities should be 1.

This is a legitimate probability assignment because the sum of the probabilities is 1.

d)

To determine

To check whether probability assignments are legitimate.

Answer to Problem 12E

Not legitimate.

Explanation of Solution

Given:

  

The conditions for probability distribution are:

1. Each of the probability lies between 0 and 1 inclusively.
2. The sum of the all probabilities should be 1.

This is not a legitimate probability assignment because there cannot be a negative probability of something occurring.

e)

To determine

To check whether probability assignments are legitimate.

Answer to Problem 12E

Legitimate.

Explanation of Solution

Given:

  

The conditions for probability distribution are:

1. Each of the probability lies between 0 and 1 inclusively.
2. The sum of the all probabilities should be 1.

This is a legitimate probability assignment because the sum of the probabilities is 1.