Stochastic Process → Poisson Process → Definition → Examples → Arrival, Inter-Arrival Times → Memoryless Property Poisson Process: Memoryless Property Memoryless property of the Poisson process can take any of the following three shapes It simply says, time and results should not be overlapped. For example, if the results of the first hour is given then the […]

Stochastic Process → Poisson Process → Definition → Examples → Arrival and Inter-Arrival Times Probability of the first Arrival Let N(t) be a Poisson process with rate . Let X1 be the time of the first arrival. Then probability of the first arrival is given by Example An office receive telephone calls according to a Poisson […]

Stochastic Process → Poisson Process → Definition → Example Questions Following are few solved examples of Poisson Process. You can take a quick revision of Poisson process by clicking here. Example 1. The number of customers arriving at a rate of 12 per hour. If it follows the Poisson process, then (a) Find the probability […]

Stochastic Process → Definition → Poisson Process → Definition Definition For fixed rate λ>0, a counting process is called a Poisson process {N(t), t∈[0,∞)} if the following three conditions are hold: 1. N(0) = 0 2. N(t) has independent occurrences 3. The occurrences in the time interval t>0 has Poisson distribution, i.e. It can be […]

Stochastic Process → Definition → Poisson Process Poisson Process is one of the most widely used counting process. It is used in conditions where some occurrences have certain rate (λ) but completely random. For example, this office receives 1000 calls per day. the earthquake occurs in this area two times per year. In this particular […]