A random sample $X_1, X_2, . . . , X_5$ is taken from a Poisson distribution with parameter λ for some λ > 0. Find the joint probability mass function in as simplified a form as possible for ($X_1, X_2, X_3, X_4, X_5$) if the observed values of the random sample are (2, 4, 0, 3, 5).

How should I approach this problem? I don't know where to start!!

  • $\begingroup$ Do you know the marginal pmf of Poisson distribution with parameter $\lambda$? Usually when the question state "A random sample ...", it means that they are independent, unless otherwise specified. $\endgroup$ – BGM Apr 15 '16 at 4:46
  • $\begingroup$ You mean this: $f(x) = e^{-λ} \frac{λ^x}{x!}$? So if the events are independent then it means that the joint probability mass function should be just the product of the marginal probability mass functions... but where dows the random sample come into play? $\endgroup$ – Ben Thompson Apr 15 '16 at 5:10
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    $\begingroup$ So the question just ask you to evaluate the joint pmf at these observed values and simplify it $\endgroup$ – BGM Apr 15 '16 at 6:29

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