https://file.aiquickdraw.com/mathbot/file/1727389384868krvu6tqp.jpg

The problem shows a uniform distribution of a random variable \( X \) between 0 and 2. A uniform distribution has a constant probability density function (PDF) over its range.

For a uniform distribution over the interval \([a, b]\), the probability density function is:
\[
f(x) = \frac{1}{b - a}
\]
where \( a = 0 \) and \( b = 2 \), so:
\[
f(x) = \frac{1}{2}
\]

The probability \( P(X > 0.72) \) can be calculated by determining the fraction of the interval from \( 0.72 \) to 2. Since \( X \) is uniformly distributed, the probability is proportional to the length of the interval.

The length of the interval from \( 0.72 \) to 2 is:
\[
2 - 0.72 = 1.28
\]

The total length of the distribution's interval is \( 2 - 0 = 2 \). Therefore, the probability is:
\[
P(X > 0.72) = \frac{1.28}{2} = 0.64
\]

Thus, the probability that \( X > 0.72 \) is \( 0.64 \).

Do you have any further questions or need additional details?

Here are some related questions for further exploration:
1. What is the cumulative distribution function (CDF) of a uniform distribution?
2. How would you calculate \( P(X < 1.5) \) for this distribution?
3. What is the expected value \( E(X) \) for this uniform distribution?
4. How do you find the variance of a uniform distribution over the interval [0, 2]?
5. How does the probability change if the range of the uniform distribution was \( [0, 4] \)?

**Tip:** In a uniform distribution, probabilities are proportional to the length of the intervals within the distribution's support.

From the uniform distribution of a random variable X given in the figure, what is P(X > 0.72)?

Learn how to calculate the probability P(X > 0.72) for a uniform distribution over the interval [0, 2]. This problem uses the uniform distribution theorem and basic probability concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation