Math Problem Statement
A random variable has uniform distribution over the interval [-1,3]. This distribution has variance equal to
a.
13/4
b.
9/2
c.
4/3
d.
8/5
Solution
For a random variable uniformly distributed over the interval , the variance is given by the formula:
Here, the interval is , so and .
Let's calculate the variance:
Thus, the variance is .
So, the correct answer is:
c.
Would you like further explanation or have any other questions?
Here are 5 follow-up questions related to this topic:
- What is the mean of a uniform distribution over an interval ?
- How do you calculate the probability density function (PDF) for a uniform distribution?
- What is the standard deviation of a uniform distribution?
- Can you compute the expected value of a uniform distribution over the interval ?
- How does the variance of a uniform distribution change if the interval length is doubled?
Tip: For a uniform distribution, the variance and the standard deviation are directly related—variance is the square of the standard deviation.
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Math Problem Analysis
Mathematical Concepts
Probability
Uniform Distribution
Variance
Formulas
Variance of Uniform Distribution: Var(X) = (b - a)^2 / 12
Theorems
Variance of Uniform Distribution
Suitable Grade Level
Grades 11-12
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