To find the expected value of a random variable, we use the formula:

$E(X) = \sum (x_i \cdot p_i)$

where:

• $x_i$ are the values the random variable can take,
• $p_i$ are the probabilities corresponding to each value $x_i$.

In the provided dataTo find the expected value of a random variable, we use the formula:

$E(X) = \sum (x_i \cdot p_i)$

where:

• $x_i$ are the values the random variable can take,
• $p_i$ are the probabilities corresponding to each value $x_i$.

In the provided

• The values $x_i$ are: $1, 2, 3, 9, 10$,
• The probabilities $p_i$ are: $0.29, 0.26, 0.22, 0.19, 0.04$.

Let's calculate the expected value:

$E(X) = (1 \cdot 0.29) + (2 \cdot 0.26) + (3 \cdot 0.22) + (9 \cdot 0.19) + (10 \cdot 0.04)$

Now I'll compute the result.

The expected value of the given random variable is $E(X) = 3.58$.

Would you like any further details on this, or do you have any other questions?

Here are five related questions to expand your understanding:

1. How is the variance of a random variable calculated?
2. What is the difference between expected value and median in statistics?
3. Can the expected value be used to predict actual outcomes?
4. How does the law of large numbers relate to expected value?
5. How would the expected value change if one of the probabilities increased?

Tip: The expected value gives a "weighted average" of all possible outcomes, where each outcome's weight is its probability.