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To calculate the expected value \( E(X) \) of a discrete random variable, we use the following formula:

\[
E(X) = \sum x_i P(x_i)
\]

Given the table with the values of \( x_i \) and \( P(x_i) \):

\[
x_i = [1, 2, 3, 4, 5]
\]
\[
P(x_i) = [0.37, 0.38, 0.04, 0.14, 0.07]
\]

Now, applying the formula:

\[
E(X) = (1 \times 0.37) + (2 \times 0.38) + (3 \times 0.04) + (4 \times 0.14) + (5 \times 0.07)
\]

Let’s compute that:

\[
E(X) = 0.37 + 0.76 + 0.12 + 0.56 + 0.35 = 2.16
\]

Thus, the expected value of the scenario is:

\[
E(X) = 2.16
\]

Would you like any further clarification or more details on this? Here are some related questions you might find interesting:

1. How is the expected value different from the median in probability?
2. What is the variance of this distribution?
3. How do you compute the expected value for continuous distributions?
4. Why is the sum of probabilities always 1 in a probability distribution?
5. Can you give an example of a scenario where the expected value doesn't represent the most likely outcome?

**Tip:** The expected value is a weighted average of all possible outcomes, but it doesn't necessarily mean it's the value most likely to occur in practice.

Calculate the expected value of the scenario.

Learn how to calculate the expected value for a discrete probability distribution with values x_i = [1, 2, 3, 4, 5] and probabilities P(x_i) = [0.37, 0.38, 0.04, 0.14, 0.07]. The step-by-step solution shows how to apply the expected value formula to get E(X) = 2.16.

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