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