Check if the Given Table Represents a Valid Probability Distribution

Math Problem Statement

Determine whether this table represents a probability distribution: X = {7, 3, 1, 8} and P(X) = {0.1, 0.25, 0.15, 0.5}

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

Non-negative probabilities: Each probability $P(X)$ must be between 0 and 1, inclusive.
Sum of probabilities equals 1: The sum of all probabilities $P(X)$ should equal 1.

From the table:

\hline X & P(X) \\ \hline 7 & 0.1 \\ 3 & 0.25 \\ 1 & 0.15 \\ 8 & 0.5 \\ \hline \end{array}$$ ### Step 1: Check Non-Negative Probabilities All probabilities $$P(X)$$ are non-negative: $$0.1, 0.25, 0.15, 0.5 \geq 0$$ So, this condition is satisfied. ### Step 2: Check Sum of Probabilities Now, let's sum the probabilities: $$0.1 + 0.25 + 0.15 + 0.5 = 1.0$$ Since the sum of the probabilities equals 1, this condition is also satisfied. ### Conclusion: Yes, this table represents a valid probability distribution. Would you like further details or have any questions? Here are 5 related questions for practice: 1. What is a probability distribution? 2. Can a probability distribution have a negative probability? 3. How do you check if a table represents a probability mass function? 4. What happens if the sum of probabilities is greater than 1? 5. How do continuous probability distributions differ from discrete ones? **Tip**: Always ensure that the total of all probabilities in any distribution sums to 1!

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Probability Distribution
Discrete Probability

Sum of probabilities: ΣP(X) = 1

Probability Distribution Theorem

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