GreenPrint said:Homework Statement
Suppose that X has an exponential distribution with mean μ. Find the probability that x lies within one standard deviation of its mean, that is find P(μ-σ≤X≤μ+σ)
Homework Equations
The Attempt at a Solution
If I'm not mistaken the standard deviation is equal to the mean of an exponential distribution so isn't the answer just zero or am I missing something important here?
The Exponential Distribution is a probability distribution that models the time between events in a process that occurs continuously and independently at a constant average rate.
The probability density function (PDF) for the Exponential Distribution is given by f(x) = λe-λx, where λ is the rate parameter and x is the time between events.
The Exponential Distribution is closely related to the Poisson Distribution, as it represents the time between events in a Poisson process. In fact, the Exponential Distribution is the continuous version of the discrete Poisson Distribution.
The Exponential Distribution has two main properties: memorylessness and the lack of a maximum value. Memorylessness means that the probability of an event occurring in the next time interval is not affected by how much time has already elapsed. The lack of a maximum value means that the distribution continues infinitely to the right.
The Exponential Distribution is commonly used to model the time between customer arrivals, the time between equipment failures, and the time between natural disasters. It is also used in queuing theory and reliability analysis.