The uniform distribution of a random variable X is given in the figure below.

From the figure, what is P(X≥0.8)?

In a uniform distribution, all outcomes are equally likely within a given interval. If we assume that the random variable \( X \) is uniformly distributed over the interval \([a, b]\), the probability density function (PDF) is constant within that interval and zero outside it.

For a uniform distribution, the probability \( P(X \geq 0.8) \) can be found using the formula:

\[
P(X \geq 0.8) = \frac{b - 0.8}{b - a}
\]

Where:
- \( a \) is the lower bound of the uniform distribution.
- \( b \) is the upper bound of the uniform distribution.
- \( 0.8 \) is the value for which we are calculating the probability.

Without the specific values of \( a \) and \( b \), I can’t provide the exact probability. However, if you provide the interval \([a, b]\) from the figure, I can compute \( P(X \geq 0.8) \) accordingly.

Do you want to upload the figure or provide the values of \( a \) and \( b \)?

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Here are some relative questions that extend this topic:
1. What is the total area under the PDF of a uniform distribution?
2. How is the mean of a uniform distribution calculated?
3. What is the variance of a uniform distribution?
4. Can you explain the significance of the cumulative distribution function (CDF) in uniform distributions?
5. How would the probability change if \( X \) were normally distributed instead of uniformly?

**Tip:** For any continuous distribution, the area under the curve of the PDF between two points gives the probability that the variable falls within that interval.

The uniform distribution of a random variable X is given in the figure below. From the figure, what is P(X≥0.8)?

Understand how to calculate P(X ≥ 0.8) for a uniform distribution with a step-by-step explanation. Explore key probability concepts, including the formula for uniform distributions and the role of the probability density function. Ideal for students in Grades 10-12.

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