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The problem asks for the expected value of a discrete random variable given its probabilities and scores. The table contains probabilities and corresponding scores, and the expected value \( E(X) \) is calculated as:

\[
E(X) = \sum (P(X_i) \cdot X_i)
\]

Where \( P(X_i) \) is the probability and \( X_i \) is the score.

Let’s compute the expected value using the given dataThe problem asks for the expected value of a discrete random variable given its probabilities and scores. The table contains probabilities and corresponding scores, and the expected value \( E(X) \) is calculated as:

\[
E(X) = \sum (P(X_i) \cdot X_i)
\]

Where \( P(X_i) \) is the probability and \( X_i \) is the score.

Let’s compute the expected value using the given 

| Probability | Scores |
|-------------|--------|
| 0.16        | 1      |
| 0.23        | 2      |
| 0.10        | 6      |
| 0.17        | 9      |
| 0.07        | 11     |
| 0.26        | 12     |
| 0.01        | 13     |

Now I will compute the expected value \( E(X) \).The expected value of the given random variable is approximately \( 6.77 \), not \( 6.44 \), which means the previous result entered was incorrect.

Do you want further details or have any questions?

Here are some related questions to expand on this topic:
1. What does the expected value represent in the context of probability?
2. How would you compute the variance for this random variable?
3. Can the expected value be negative? If yes, in which situations?
4. How do you interpret the expected value in real-world situations?
5. How does the law of large numbers relate to expected value?

**Tip:** The expected value is often considered the "long-run average" outcome of a random variable.

Find the expected value of the above random variable.

Learn how to compute the expected value of a discrete random variable using a probability table. This example uses probabilities and corresponding scores to calculate the expected value using the formula E(X) = Σ(P(X_i) * X_i). Suitable for students in Grades 10-12.

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