Concept explainers
a)
To check whether probability assignments are possible.
a)
Answer to Problem 11E
Yes, possible.
Explanation of Solution
Given:
Red | Yellow | Green | Blue | Total | |
a | 0.25 | 0.25 | 0.25 | 0.25 | 1 |
b | 0.1 | 0.2 | 0.3 | 0.4 | 1 |
c | 0.2 | 0.3 | 0.4 | 0.5 | 1.4 |
d | 0 | 0 | 1 | 0 | 1 |
e | 0.1 | 0.2 | 1.2 | -1.5 | 0 |
The conditions for probability distribution are:
- Each of the probability lies between 0 and 1 inclusively.
- The sum of the all probabilities should be 1.
Both the conditions satisfied hence, there are possible probability assignments.
b)
To check whether probability assignments are possible.
b)
Answer to Problem 11E
Yes, possible.
Explanation of Solution
Given:
Red | Yellow | Green | Blue | Total | |
a | 0.25 | 0.25 | 0.25 | 0.25 | 1 |
b | 0.1 | 0.2 | 0.3 | 0.4 | 1 |
c | 0.2 | 0.3 | 0.4 | 0.5 | 1.4 |
d | 0 | 0 | 1 | 0 | 1 |
e | 0.1 | 0.2 | 1.2 | -1.5 | 0 |
The conditions for probability distribution are:
- Each of the probability lies between 0 and 1 inclusively.
- The sum of the all probabilities should be 1.
Both the conditions satisfied hence, there are possible probability assignments.
c)
To check whether probability assignments are possible.
c)
Answer to Problem 11E
Not possible.
Explanation of Solution
Given:
Red | Yellow | Green | Blue | Total | |
A | 0.25 | 0.25 | 0.25 | 0.25 | 1 |
B | 0.1 | 0.2 | 0.3 | 0.4 | 1 |
C | 0.2 | 0.3 | 0.4 | 0.5 | 1.4 |
D | 0 | 0 | 1 | 0 | 1 |
E | 0.1 | 0.2 | 1.2 | -1.5 | 0 |
The conditions for probability distribution are:
- Each of the probability lies between 0 and 1 inclusively.
- The sum of the all probabilities should be 1.
The sum of the probabilities for part c is 1.4 which is greater than 1. Hence, it does not possible.
d)
To check whether probability assignments are possible.
d)
Answer to Problem 11E
Yes, possible.
Explanation of Solution
Given:
Red | Yellow | Green | Blue | Total | |
A | 0.25 | 0.25 | 0.25 | 0.25 | 1 |
B | 0.1 | 0.2 | 0.3 | 0.4 | 1 |
C | 0.2 | 0.3 | 0.4 | 0.5 | 1.4 |
D | 0 | 0 | 1 | 0 | 1 |
E | 0.1 | 0.2 | 1.2 | -1.5 | 0 |
The conditions for probability distribution are:
- Each of the probability lies between 0 and 1 inclusively.
- The sum of the all probabilities should be 1.
Both the conditions satisfied hence, there are possible probability assignments.
e)
To check whether probability assignments are possible.
e)
Answer to Problem 11E
Not possible.
Explanation of Solution
Given:
Red | Yellow | Green | Blue | Total | |
A | 0.25 | 0.25 | 0.25 | 0.25 | 1 |
B | 0.1 | 0.2 | 0.3 | 0.4 | 1 |
C | 0.2 | 0.3 | 0.4 | 0.5 | 1.4 |
D | 0 | 0 | 1 | 0 | 1 |
E | 0.1 | 0.2 | 1.2 | -1.5 | 0 |
The conditions for probability distribution are:
- Each of the probability lies between 0 and 1 inclusively.
- The sum of the all probabilities should be 1.
The probabilities are less than 0 and greater than 1. Hence, it does not possible.
Chapter 14 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
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