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Suppose that the number of accidents occurring at a particular intersection each week is a Poisson random variable. It is estimated that the probability of having at least one accident in a week, at the intersection, is 0.98.

Calculate the average number of accidents occurring each week at the intersection.

Thanks in advance for the help!

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    $\begingroup$ Sounds rather like homework; if so give it the homework tag. $\endgroup$
    – Karl
    Commented Oct 2, 2011 at 18:34

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Hint: if you knew the average, you could determine the probability of having exactly 0, exactly 1, exactly 2, and so forth.

So, what you need to do is rearrange the equation that you use so that if you know what you know (probability of 1+ accidents =.98) you can determine the average.

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  • $\begingroup$ Wow, that was extremely helpful! Just to make sure I understand it all correctly, I can say that the P(X=0) = 1 - P(X >= 1) = 0.2, and from there I can plug it in the equation: 0.2 = ((x^0)/0!)*e^(-x) and solve for x. $\endgroup$ Commented Oct 3, 2011 at 3:27
  • $\begingroup$ I actually made it confusing in that equation, the x's in the equation should be a different variable to differ from the random variable x=0. $\endgroup$ Commented Oct 3, 2011 at 3:39

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