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Probability : Poisson, Random Variable, Value and Variance

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.


Solution Summary

Poisson random variables, value and variance are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.