Final answer:
The student's question pertains to the exponential distribution in the context of statistics, where they are dealing with a random variable X that is exponentially distributed with a rate parameter of 2.5. This concept is typically covered in college-level mathematics or statistics courses.
Step-by-step explanation:
The student is asking about how to work with the exponential distribution, a concept in statistics. Specifically, they mention a random variable X that follows an exponential distribution with a rate parameter λ (lambda) equal to 2.5. The exponential distribution is heavily used to model the time between events in a Poisson process and has a clear memoryless property.
For example, if X represents the amount of time a postal clerk spends with a customer and we know that this time is exponentially distributed with λ = 2.5, then we can calculate various probabilities associated with this variable, like the probability that a clerk spends more than a certain amount of time with a customer or within a certain time interval.
In general, for an exponential distribution with rate parameter λ, the probability density function (PDF) is f(x) = λ e^(-λx), and the cumulative distribution function (CDF) is P(X ≤ x) = 1 - e^(-λx). These functions are used to determine probabilities and other characteristics of the distribution, such as the mean and standard deviation, with the mean being the reciprocal of λ (1/λ).