Final answer:
The Weibull density function simplifies to an exponential distribution when alpha equals 1, which expresses a constant rate of events over time.
Step-by-step explanation:
The student's question revolves around a specific instance of the Weibull density function when α (alpha) equals 1. In probability and statistics, the Weibull density function is used to describe the distribution of lifetimes of objects. When α = 1, this function simplifies to an exponential distribution, which can be expressed as f(x; λ) = λ * e^{-λ x} for x ≥ 0, where λ is the rate parameter. The area under this probability density function over the interval from 0 to ∞ is 1, satisfying the property of a probability density function (pdf), which is to quantify the probabilities of different outcomes in a continuous random variable scenario. When Weibull's scale parameter α is set to 1, the distribution represents a scenario where events occur at a constant rate.