Find the expected value E(X)
 of the following data. Round your answer to one decimal place.

x	2
3
4
5
6
P(X=x)
0.3
0.1
0.2
0.1
0.3



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

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

Given the dataTo find the expected value \( E(X) \) of a random variable \( X \), we use the formula:

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

Given the 

- \( x = 2, 3, 4, 5, 6 \)
- \( P(X = x) = 0.3, 0.1, 0.2, 0.1, 0.3 \)

We compute the expected value as follows:

\[
E(X) = (2 \cdot 0.3) + (3 \cdot 0.1) + (4 \cdot 0.2) + (5 \cdot 0.1) + (6 \cdot 0.3)
\]

Calculating each term:

\[
E(X) = 2(0.3) + 3(0.1) + 4(0.2) + 5(0.1) + 6(0.3)
\]
\[
E(X) = 0.6 + 0.3 + 0.8 + 0.5 + 1.8
\]
\[
E(X) = 4.0
\]

So, the expected value \( E(X) \) is **4.0**.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How is the concept of expected value used in decision-making?
2. How does changing the probabilities affect the expected value?
3. What is the significance of expected value in probability theory?
4. How would you calculate the variance of \( X \) based on this data?
5. How does the expected value differ for continuous vs. discrete random variables?

**Tip:** The expected value gives a long-run average of outcomes weighted by their probabilities.

Find the expected value E(X) of the following data. Round your answer to one decimal place.
x: 2, 3, 4, 5, 6
P(X=x): 0.3, 0.1, 0.2, 0.1, 0.3

Learn how to calculate the expected value of a discrete probability distribution with data points x = 2, 3, 4, 5, 6 and their probabilities P(X=x) = 0.3, 0.1, 0.2, 0.1, 0.3. This problem demonstrates the use of the expected value formula and covers important probability concepts. Suitable for students in Grades 9-12.

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