Math Problem Statement
Determine whether this table represents a probability distribution.
Solution
To determine if the given table represents a probability distribution, we need to check two key conditions:
- Non-negativity: Each probability must be greater than or equal to zero.
- Total Probability: The sum of all probabilities must equal 1.
Here is the table provided:
\hline x & P(x) \\ \hline 0 & 0.25 \\ 1 & 0.3 \\ 2 & 0.25 \\ 3 & 5.5511151231258 \times 10^{-17} \\ \hline \end{array}$$ Let's check the conditions: - **Non-negativity**: All the $$P(x)$$ values are non-negative. The last probability value, $$5.5511151231258 \times 10^{-17}$$, is a very small positive number (close to zero but still non-negative). - **Total Probability**: The sum of all probabilities is: $$0.25 + 0.3 + 0.25 + 5.5511151231258 \times 10^{-17} = 0.8 + 0.2 \times 10^{-16} \approx 0.8$$ Since the sum of the probabilities is not equal to 1, **this is not a valid probability distribution**. Therefore, the correct answer is: - No, it is not a probability distribution. Would you like any further details or clarifications? Here are 5 related questions to expand your understanding: 1. What are the requirements for a valid probability distribution? 2. How would you correct the given table to make it a valid probability distribution? 3. Why must the sum of probabilities in a distribution always equal 1? 4. Can a probability value be negative? Why or why not? 5. What happens if the sum of probabilities exceeds 1? **Tip**: When checking for a valid probability distribution, always verify both non-negativity and that the total sum equals 1.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Probability Distribution
Non-negativity
Sum of Probabilities
Formulas
Sum of P(x) = 1
Theorems
Probability Distribution Theorem
Suitable Grade Level
Grades 9-12
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