Math Problem Statement

Does the following table represent a valid discrete probability distribution?

Solution

To determine whether the given table represents a valid discrete probability distribution, we must check two conditions:

  1. Non-negativity: All probabilities should be non-negative.
  2. Sum of probabilities: The sum of all probabilities must equal 1.

From the table:

  • Probabilities: 0.11,0.06,0.25,0.41,0.510.11, 0.06, 0.25, 0.41, 0.51

Let's sum these probabilities to check if they equal 1:

0.11+0.06+0.25+0.41+0.51=1.340.11 + 0.06 + 0.25 + 0.41 + 0.51 = 1.34

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:

  1. What are the properties of a valid probability distribution?
  2. How can you adjust probabilities to create a valid distribution?
  3. What happens if the sum of probabilities is less than 1?
  4. Can probabilities ever be negative in a valid distribution?
  5. 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.

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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