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.