Final answer:
Continuous probability functions depict the likelihood of outcomes within a continuous range of values. Probabilities are determined by the area under the pdf curve for a given interval. Single values have a probability of zero, as do values outside the defined range of the function.
Step-by-step explanation:
In the context of probability and calculus, the given scenarios outline various continuous probability functions and associated probability calculations. Continuous probability distributions provide a model where the outcome is a continuous range of values, and the probability of any single outcome is zero. Instead, you calculate the probability of a range of outcomes by finding the area under the curve of the probability density function (pdf) between two points. For example, the function f(x) = 1/10 for 0 ≤ x ≤ 10 represents a uniform distribution, where all outcomes within the range are equally likely. To find the probability of the event 0 < x < 4, you would calculate the area under the function f(x) between x = 0 and x = 4.
For a continuous distribution, the probability of any single precise value, such as P(x = 7), is zero because the area under the curve at a single point is zero. Similarly, the probability for a value outside the defined range, such as P(x > 15) when the function is defined only up to x = 15, is also zero. These principles are central to understanding how to work with continuous probability functions.