Final answer:
The exponential distribution is a continuous probability distribution used to model time until an event occurs, with widespread applications across various fields.
Step-by-step explanation:
The exponential probability distribution is used to model the time until a certain event occurs. This type of distribution is continuous and is particularly useful for describing random processes in various fields such as engineering, physics, and environmental science. The distribution is characterized by a decay parameter m, which is inversely related to the mean (μ) of the distribution, that is m = 1/μ. The mean is also equal to the standard deviation in this distribution. The probability density function (PDF) of an exponential distribution is f(x) = me-mx, where x ≥ 0, and the cumulative distribution function (CDF) is P(X ≤ x) = 1 - e-mx.
Real-word applications of the exponential distribution include modeling the length of long-distance phone calls, the intervals between arrivals at a hospital ER, and product reliability such as the lifetime of a car battery. It has a 'memoryless' property, which implies that the probability of the event occurring in the future is independent of any past occurrences.