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Poisson distribution. E(X) not a whole number.

  1. Sep 28, 2013 #1
    1. The problem statement, all variables and given/known data
    During the day, cars pass along a point on a remote road at an average rate of one per 20 minutes.

    Calculate the probability that;

    (i) in the course of an hour no car passes;
    (ii) in the course of 30 minutes exactly 4 cars pass;


    2. Relevant equations

    [itex]P(X = x) = \frac{e^{-\lambda}\lambda^{x}}{x!}[/itex]

    3. The attempt at a solution

    [itex]\lambda = 3[/itex]

    [itex]P(X = 0) = e^{-3} = 0.0497[/itex]


    My question: In part 2 [itex]\lambda = 1.5[/itex]. Can [itex]\lambda[/itex] be a Real number or must it be an integer? I assume it can be any number as [itex] E(X) [/itex] does not necessarily have to be in the support of X.

    Thanks.
     
  2. jcsd
  3. Sep 28, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    λ can be any non-negative real number.
     
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