132k views
3 votes
The exponential distribution is related to the poisson distribution.

User Barn
by
7.9k points

1 Answer

3 votes

Final answer:

The Poisson distribution is connected to the exponential distribution through their relationship with the timing of events and occurrence rates, with each being applicable under inverse circumstances.

Step-by-step explanation:

The relationship between the Poisson distribution and the exponential distribution is a fundamental concept in probability theory. If the time between successive events follows an exponential distribution with a mean of μ units of time and times between events are independent, then the number of events per unit time follows a Poisson distribution with a mean λ = 1/μ. Conversely, if the number of events per unit time follows a Poisson distribution, then the time between events follows an exponential distribution.

Examples of Poisson experiments include the number of misspelled words in a book or the number of occurrences within a fixed time interval. For the exponential distribution, examples might include the duration of phone calls or the lifetime of a product. Both distributions are useful for different types of random events and are interconnected.

To approximate a binomial distribution with a Poisson distribution, the probability of success should be low (p ≤ .05) and the number of trials should be high (n ≥ 20). This approximation is related to both distributions' tendency to deal with rare events over many trials or long time intervals.

User Marlon Patrick
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.