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

  • #1
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1

Homework Statement


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;


Homework Equations



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

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.
 

Answers and Replies

  • #2
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λ can be any non-negative real number.
 
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