Math Problem Statement
Solution
To determine whether the given table represents a valid discrete probability distribution, we must check two conditions:
- Non-negativity: All probabilities should be non-negative.
- Sum of probabilities: The sum of all probabilities must equal 1.
From the table:
- Probabilities:
Let's sum these probabilities to check if they equal 1:
Since the sum of probabilities is greater than 1, this table does not represent a valid discrete probability distribution.
Would you like more details, or do you have any questions?
Here are some related questions:
- What are the properties of a valid probability distribution?
- How can you adjust probabilities to create a valid distribution?
- What happens if the sum of probabilities is less than 1?
- Can probabilities ever be negative in a valid distribution?
- What is the significance of the total sum being exactly 1?
Tip: Always verify that the sum of probabilities in a distribution is exactly 1 to ensure its validity.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Discrete Probability Distribution
Formulas
Sum of probabilities in a discrete distribution = 1
Theorems
Non-negativity of probabilities
Sum of probabilities must equal 1
Suitable Grade Level
Grades 9-12
Related Recommendation
Determine if a Table Represents a Discrete Probability Distribution
Check if the Given Table Represents a Valid Probability Distribution
Does This Table Represent a Probability Distribution?
Valid Probability Distribution: Checking the Table
Determine if the Given Table Represents a Probability Distribution