# Another poisson distribution question

• romeo6
In summary, the most probable month for the third event to occur, given that the mean time between events is 6 months, would be the 18th month. To calculate this, you would need to find the probability density function (p.d.f.) and the cumulative distribution function (c.d.f.) of the third event occurring within a given time frame. The expected value of the p.d.f. would then give you the most probable month for the third event to occur.
romeo6
Ok,

If the mean time between a single random event occurring is 6 months then is the most probably month for the third event to occur the 18th month?

Thanks!

I don't know the answer but here's how I'd go about it. You need to calculate the probability density function (p.d.f.) of the third event occurring within a given time frame. Start from the basics, e.g. the corresponding cumulative distribution function (c.d.f.) will be Prob{third event < t} = Prob{event "one" < t and event "two" < t and event "three" < t} = Prob{event "one" < t} Prob{event "two" < t} Prob{event "three" < t}. Once you calculate the c.d.f., you can then figure out the p.d.f. The expected value of that p.d.f. is your answer.

Last edited:

Yes, that is correct. According to the Poisson distribution, the expected number of events in a given time interval is equal to the mean rate of events multiplied by the length of the interval. In this case, the mean time between events is 6 months, so the expected number of events in 18 months would be 3. Therefore, the most probable month for the third event to occur would be the 18th month. However, it is important to note that this is only a prediction based on the Poisson distribution and there is still a possibility for the event to occur in a different month.

## 1. What is a Poisson distribution?

A Poisson distribution is a probability distribution that is used to model the number of occurrences of a certain event in a fixed interval of time or space, given that these occurrences are independent and rare.

## 2. How is a Poisson distribution different from a normal distribution?

A normal distribution is used to model continuous data, while a Poisson distribution is used for discrete data. Additionally, the shape of a Poisson distribution is skewed to the right, while a normal distribution is symmetrical.

## 3. What are the parameters of a Poisson distribution?

The parameters of a Poisson distribution are the mean, denoted by λ (lambda), and the interval of time or space, denoted by t. These parameters determine the shape and characteristics of the distribution.

## 4. When should a Poisson distribution be used?

A Poisson distribution should be used when the data being modeled is discrete and the occurrences are independent and rare. It is commonly used in fields such as biology, finance, and telecommunications.

## 5. How is the Poisson distribution related to the Poisson process?

The Poisson distribution is used to model the number of occurrences in a fixed interval, while the Poisson process is a stochastic process that models the time between occurrences. The two are closely related and often used together to analyze data and make predictions.

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