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# Probability : Poisson, Random Variable, Value and Variance

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1. Suppose that the number of eggs laid on a tree leaf by a particular type of insect is a Poisson random variable with l = 1.

(a) What is the probability that any particular leaf will have at least two eggs?

(b) Suppose that a person searches through leaves on a tree until he finds one with at least two eggs. Letting X = the number of leaves searched, what is the expected value and variance of X?

*Please specify the terms you use (if necessary) and explain each step of your solutions.

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#### Solution Summary

Poisson random variables, value and variance are investigated and discussed. The solution is detailed and well presented. T

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