eksponenttijakautuma
Eksponenttijakautuma, also known as exponential distribution, is a continuous probability distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is widely used in various fields such as reliability engineering, queuing theory, and survival analysis.
The probability density function (PDF) of an exponential distribution is given by:
f(x; λ) = λ * e^(-λx), for x ≥ 0
where λ (lambda) is the rate parameter, which is the inverse of the mean. The cumulative distribution
F(x; λ) = 1 - e^(-λx), for x ≥ 0
Key properties of the exponential distribution include:
1. Memorylessness: The exponential distribution is memoryless, meaning that the probability of an event occurring in
2. Mean and variance: The mean (μ) and variance (σ^2) of an exponential distribution are both equal
3. Sum of exponentials: The sum of n independent exponential random variables, each with rate λ, follows
The exponential distribution is often used to model the time until the next event occurs, such as