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Two-dimensional PoisSOn process is process of randomly occurring special points in the plane such thatFor any region of area A the number of special points in that ...

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Two-dimensional PoisSOn process is process of randomly occurring special points in the plane such thatFor any region of area A the number of special points in that region has Poisson distri- bution with mean AA andthe number of special points in nOn-overlapping regions is independent_ For such process consider an arbitrary location in the plane and let X denote its distance from its nearest special point where distance is measured in the USHAl Euclidean HAICT )_ Find P{X > t} (6) Find E{X} Le

two-dimensional PoisSOn process is process of randomly occurring special points in the plane such that For any region of area A the number of special points in that region has Poisson distri- bution with mean AA and the number of special points in nOn-overlapping regions is independent_ For such process consider an arbitrary location in the plane and let X denote its distance from its nearest special point where distance is measured in the USHAl Euclidean HAICT )_ Find P{X > t} (6) Find E{X} Let N(t) be the number of points in ballwith center (0,0) aUId radius t. For > ( E{N(s) | N(t) =n}



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Let $X$ be a Poisson random variable with parameter $\lambda=5$ Compute the probabilities $p_{0}, \ldots, p_{6}$ to four decimal places.


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