Final answer:
The student's question revolves around calculating probabilities for continuous uniform distributions. To find the probability of an interval, you calculate the area under the PDF over that interval. For a constant PDF, this equals the product of the interval's width and the constant function value, normalized if necessary.
Step-by-step explanation:
The student seems to have a question related to continuous probability distributions, specifically regarding uniform distributions and how to calculate probabilities within certain intervals. To calculate probabilities for these types of functions, one must integrate the probability density function (PDF) over the desired interval. However, if the PDF is constant (as in a uniform distribution), the probability is equal to the area of the rectangle formed by the height of the PDF and the width of the interval.
For example, to find P(0 < x < 4) for a function described by f(x) = 1 for 0 ≤ x ≤ 10, you would simply calculate the area of the rectangle with height 1 and width 4, yielding a probability of 0.4 (since the total area under the curve must be 1 for a probability distribution).
Similarly, if f(x) is a continuous probability function equal to 12 over the interval 0 ≤ x ≤ 12, then P(0 < x < 12) would be the area of the rectangle with height 12 and width 12, which must be normalized because the total area under a probability distribution must equal 1. Hence, each point would have a probability of 1/12 over this interval, since 12 (height) × 12 (width) = 144 and 1/144 (each point's probability) × 144 (total number of points) = 1.
Ultimately, these questions serve as foundational concepts in understanding uniform distributions and calculating probabilities.