Final answer:
In probability theory, the probability density function (PDF) is used to describe probabilities for continuous random variables. For a continuous random variable, we calculate the probability of the value falling within a specific range, rather than the probability of the value being equal to a specific value.
Step-by-step explanation:
In probability theory, the probability density function (PDF) is used to describe probabilities for continuous random variables. For a continuous random variable, we calculate the probability of the value falling within a specific range, rather than the probability of the value being equal to a specific value. This is because the probability of a continuous random variable taking on any single value is always zero. Instead, we calculate the probability that the value of the random variable is between two values, denoted as P(a < x < b), where a and b are the lower and upper bounds of the range.