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I'm slightly confused with when I should use a Poisson distribution.

If I have a case where:

  • I have the sample mean of the number of events happening in a particular day (say it is 1.27).
  • Five days are randomly selected from a sample.

Can I use the Poisson process to find the probability that the sample mean now is more than 0.3?

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  • $\begingroup$ I'm not completely sure I understand your description, but it sounds like you're trying to construct some kind of interval for a Poisson mean for some unobserved time period based on a sample for some other time period. Is that correct? $\endgroup$ – Glen_b -Reinstate Monica Feb 20 '14 at 13:53
  • $\begingroup$ Thanks for the speedy reverts Glen. I'm not quite sure if Poisson is the game here. What i have on hand is a probability distribution of the number of events happening on a particular day - from which I've worked out the mean. What i want to find out is the probability that this mean is going to be more than 0.3 if 4 days are randomly selected from a sample. Is the sample size important? $\endgroup$ – user1275515 Feb 20 '14 at 14:01
  • $\begingroup$ Oh, I think I see. You've been given some probability distribution for a random variable representing the number of events per day. You computed the mean of that distribution (a population mean). Then you start talking about a sample mean over several days of observations. Is that it? (There are several strange things about your wording that make it especially confusing.) $\endgroup$ – Glen_b -Reinstate Monica Feb 20 '14 at 14:30
  • $\begingroup$ Spot on Glen! You're really brilliant. Yeps. Thats what Im trying to self learn and solve $\endgroup$ – user1275515 Feb 20 '14 at 14:35
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    $\begingroup$ I will say that there's no hint in the little information you give that the Poisson comes into this at all. A little more detail might clarify that. $\endgroup$ – Glen_b -Reinstate Monica Feb 20 '14 at 22:33
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Here is how I understand the Poisson distribution: the distribution is used to describe events happening over a given range(i.e. a time period)

For the PDF distribution you can use it for things like the probabilities for:

  • Number of mutation in DNA strands per unit of time.

  • N peaks in stock in a over a given period of time

For the CDF distribution you can use it for the probabilities of:

  • 3 or less robberies in a given length of time.
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