https://file.aiquickdraw.com/mathbot/file/1728167658911crv3slo6.jpg

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

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

From the image, the values of \( X \) and their corresponding probabilities \( P(X = x_i) \) are:

- For \( X = -5 \), \( P(X = -5) = 0.2 \)
- For \( X = 0 \), \( P(X = 0) = 0.4 \)
- For \( X = 5 \), \( P(X = 5) = 0.4 \)

Now, let's compute the expected value:

\[
E(X) = (-5 \cdot 0.2) + (0 \cdot 0.4) + (5 \cdot 0.4)
\]

\[
E(X) = (-1) + (0) + (2)
\]

\[
E(X) = 1
\]

So, the expected value \( E(X) \) is 1.

Would you like further details or have any questions?

Here are five related questions:
1. How is the expected value different from the median in a probability distribution?
2. What does the expected value represent in practical scenarios?
3. How can the variance of \( X \) be computed from this distribution?
4. What happens to the expected value if the probabilities are changed?
5. What is the impact of adding a constant to each \( x_i \) on the expected value?

**Tip:** The expected value is often thought of as the "average" outcome if you could repeat the experiment many times.

What is the expected value of the discrete random variable X given the probability distribution from the graph?

Learn how to calculate the expected value of a discrete random variable using its probability distribution. The problem involves a variable X with values -5, 0, and 5 and corresponding probabilities 0.2, 0.4, and 0.4. Suitable for students in Grades 10-12.

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