Math Problem Statement

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

Solution

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

E(X)=a+b2E(X) = \frac{a + b}{2}

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

E(X)=0+6.12=6.12=3.05E(X) = \frac{0 + 6.1}{2} = \frac{6.1}{2} = 3.05

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

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Math Problem Analysis

Mathematical Concepts

Probability
Uniform Distribution

Formulas

Expected Value of Uniform Distribution

Theorems

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Suitable Grade Level

Advanced High School