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Let X be the number of cars per minute passing a certain point of some road...

  1. Let X be the number of cars per minute passing a certain point of some road between 8 A.M. and 10 A.M. on a Sunday. Assume that X has a Poisson distribution with mean 5. Find the probability of observing 4 or fewer cars during any given minute.

Why do I have to use P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) instead of 1-P(X=5) for the solution?

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Answer #1

Why do I have to use P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) instead of 1-P(X=5) for the solution?

  • here, the sample size (n) is unknown. You have considered mean=5 as a sample size which is incorrect.
  • when sample size (n) is known, This will be a case of binomial distribution. In this case, 1-P(X=5) can be used.

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