# 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

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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