
Let X~U[0,6.1], what is E(X)? Give answer to 2 decimal places.

For a random variable \( X \) uniformly distributed on the interval \( [a, b] \), the expected value \( E(X) \) is calculated using the formula:

\[
E(X) = \frac{a + b}{2}
\]

In this case, \( X \sim U[0, 6.1] \), so \( a = 0 \) and \( b = 6.1 \). Plugging these values into the formula:

\[
E(X) = \frac{0 + 6.1}{2} = \frac{6.1}{2} = 3.05
\]

Thus, \( E(X) = 3.05 \).

Let me know if you'd like more details or additional questions on uniform distribution.

Here are related questions:
1. How do you calculate the variance of \( X \) for a uniform distribution?
2. What is the probability density function (PDF) of a uniform distribution?
3. How does the uniform distribution differ from other continuous distributions?
4. What is the cumulative distribution function (CDF) for a uniform distribution?
5. How is a uniform distribution used in simulation models?

**Tip:** For a uniform distribution, the mean is always halfway between the minimum and maximum values of the interval.

Learn how to calculate the expected value E(X) for a uniform distribution U[0, 6.1] with a detailed step-by-step solution. This problem covers key probability concepts, including the formula for the expected value of a uniform distribution. Suitable for advanced high school students and anyone interested in probability theory.

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