Math Problem Statement

Determine whether this table represents a probability distribution: x = {0, 1, 2, 3}, P(x) = {0, 0.25, 0.15, 0.6}

Solution

To determine if the given table represents a probability distribution, we need to verify two conditions:

  1. Non-negative probabilities: All the values of P(x)P(x) must be between 0 and 1, inclusive.
  2. Sum of probabilities equals 1: The total of all P(x)P(x) values must add up to 1.

Let's check these conditions for the provided table:

xxP(x)P(x)
00
10.25
20.15
30.6
  1. Non-negative probabilities: All P(x)P(x) values are between 0 and 1, so the first condition is satisfied.

  2. Sum of probabilities: 0+0.25+0.15+0.6=10 + 0.25 + 0.15 + 0.6 = 1 The sum is exactly 1, so the second condition is also satisfied.

Conclusion:

Yes, this table does represent a probability distribution.

Would you like further explanation or details?

Here are 5 related questions you might find helpful:

  1. What other types of probability distributions exist?
  2. How can probability distributions be used in real-world scenarios?
  3. What is the difference between discrete and continuous probability distributions?
  4. How do you calculate the expected value of a probability distribution?
  5. What are the properties of a binomial probability distribution?

Tip: When checking for a valid probability distribution, always ensure that the sum of all probabilities equals exactly 1!

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Math Problem Analysis

Mathematical Concepts

Probability Distributions

Formulas

Sum of probabilities: ΣP(x) = 1

Theorems

Probability Distribution Theorem

Suitable Grade Level

Grades 10-12