Probability of event modelled by poisson happening twice, consecutively

In summary, the problem involves finding the probability of receiving at least three telephone calls in each of two successive one-minute intervals, given that the number of calls per minute follows a Poisson distribution with a mean of 3.5. One approach is to multiply the probability of at least three calls in one interval by itself, considering that both intervals need to have at least three calls for the event to occur.
  • #1
cmkluza
118
1
I'm not great at statistics, so I don't know where to start with this problem. It is stated as follows:

The number of telephone calls, T, received each minute can be modeled by a Poisson distribution with a mean of 3.5.

Find the probability that at least three telephone calls are received in each of two successive one-minute intervals.

So, I understand we have T ~ Po(3.5), and using a calculator or formula, I could easily identify the probability of having at least three telephone calls, but I don't understand what to do about that two successive part. Been thinking on this one for a while, but I'm at a loss as to what to do. Can anyone give me any suggestions on how to think about this to arrive at an answer?
 
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  • #2
You could multiply the probability of atleast 3 successive calls twice i.e P(\(\displaystyle \ge\) 3 phone calls) x P(\(\displaystyle \ge\) 3 phone calls), since our event gets completed only if we consider both of it's elements(in this case, the number of calls in two successive minutes).

This is just my suggestion as I, myself, am certainly not an ace in the area of statistics.
 

FAQ: Probability of event modelled by poisson happening twice, consecutively

What is the Poisson distribution?

The Poisson distribution is a probability model that is used to describe the likelihood of a certain number of events occurring within a specific period of time or within a given area. It is often used to model rare events that occur randomly.

What does it mean to have an event happen twice, consecutively?

Having an event happen twice, consecutively means that the same event occurs two times in a row, without any other events happening in between.

How is the probability of an event happening twice, consecutively calculated using the Poisson distribution?

The probability of an event happening twice, consecutively can be calculated by multiplying the probability of the event happening once by itself. In other words, if the probability of the event happening once is p, then the probability of it happening twice, consecutively is p x p, or p2.

What assumptions are made when using the Poisson distribution to model the probability of an event happening twice, consecutively?

The assumptions made when using the Poisson distribution include that the events occur randomly and independently of each other, and that the probability of the event occurring is the same for each time interval or area considered.

Can the Poisson distribution be used to model the probability of an event happening more than twice, consecutively?

Yes, the Poisson distribution can be used to model the probability of an event happening any number of times consecutively, as long as the assumptions of the distribution are met. The probability of an event happening three times consecutively would be p3, four times would be p4, and so on.

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