What is the expected value of the random variable X is X~Uniform(3,6,11,4)?

(Give the answer with 2 decimal values)

The expected value \( E(X) \) of a random variable \( X \) with a uniform distribution over a set of values is the arithmetic mean of those values. In this case, the random variable \( X \) can take the values \( \{3, 6, 11, 4\} \).

The formula for the expected value is:

\[
E(X) = \frac{1}{n} \sum_{i=1}^{n} X_i
\]

where \( X_i \) are the values that \( X \) can take, and \( n \) is the total number of values.

Given that \( X \) can take the values \( 3, 6, 11, 4 \), and there are 4 values, we calculate:

\[
E(X) = \frac{1}{4} (3 + 6 + 11 + 4) = \frac{1}{4} \times 24 = 6.00
\]

Thus, the expected value of \( X \) is:

\[
E(X) = 6.00
\]

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:
1. How would the expected value change if one of the values is removed from the set?
2. What is the variance of \( X \) for this uniform distribution?
3. How would the expected value formula change for a continuous uniform distribution?
4. How is the expected value different from the median in this case?
5. Can you find the probability of each value for this discrete uniform distribution?

**Tip:** The expected value gives you the "center" of a distribution but does not tell you about the spread or variability, which is described by variance or standard deviation.

What is the expected value of the random variable X is X~Uniform(3,6,11,4)?

Calculate the expected value of a random variable X with a uniform distribution over the values {3, 6, 11, 4}. The solution covers key statistical concepts such as the arithmetic mean and expected value. Suitable for students in Grades 9-12.

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