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To compute the expectation (also known as the expected value) for the experiment described in the table, we can use the formula for expected value:

\[
E(X) = \sum (x_i \cdot p_i)
\]

Where:
- \( x_i \) is the outcome
- \( p_i \) is the probability of each outcome

The outcomes and probabilities provided are:

- Outcome 5: Probability 0.5
- Outcome 6: Probability 0.14
- Outcome 7: Probability 0.2
- Outcome 8: Probability 0.08
- Outcome 9: Probability 0.06
- Outcome 10: Probability 0.02

Let's compute the expectation:

\[
E(X) = (5 \cdot 0.5) + (6 \cdot 0.14) + (7 \cdot 0.2) + (8 \cdot 0.08) + (9 \cdot 0.06) + (10 \cdot 0.02)
\]

I'll calculate this now.The expected value for this experiment is \( E(X) = 6.12 \).

Would you like further details or have any questions?

Here are some related questions for deeper understanding:
1. What does the expected value represent in a probability distribution?
2. How would the expected value change if the probabilities were different?
3. What is the difference between expected value and variance?
4. How would you calculate the variance for this data set?
5. What are some real-life applications of calculating expected value?

**Tip:** Expected value helps to determine the long-term average outcome of a random experiment, useful in decision-making processes.

The outcomes of an experiment and the probability of each outcome are given in the table below. Compute the expectation for this experiment.

Learn how to calculate the expected value from a probability distribution table. This problem covers key probability concepts and uses the expected value formula. Suitable for students in Grades 9-12.

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