3. Consider n independent observations X1,..., X, of a Poisson random variable with param-eter A.(a) Use Chebyshev's inequality to evaluate the minimum number of observations neededto achieveп1P(|Xn– A|< 0.01) > 0.9,where XnΣΧ.пi=1(b) Repeat the computations using the Central Limit Theorem.Note:Remember that the Poisson distribution is a discrete distribution with PMFfx(x;A) =х!where xe {0,1,2,3, .}, and 1 > 0and hence E(X) = A , and Var (X) = A.

Consider n independent observations X1,...,Xn of a Poisson random variable with parameter λ

3. Consider n independent observations X1,..., X, of a Poisson random variable with param- eter 1. (a) Use Chebyshev's inequality to evaluate the minimum number of observations needed to achieve 1 Xị. i=1 P(|Xn- A| < 0.01) > 0.9, where Xn n (b) Repeat the computations using the Central Limit Theorem. Note: Remember that the Poisson distribution is a discrete distribution with PMF fx(x; A) х! where xe {0,1,2,3,……}, and 1 > 0 and hence E(X) = A , and Var(X) = A.

3. Consider n independent observations X1,..., X, of a Poisson random variable with param- eter 1. (a) Use Chebyshev's inequality to evaluate the minimum number of observations needed to achieve 1 Xị. i=1 P(|Xn- A| < 0.01) > 0.9, where Xn n (b) Repeat the computations using the Central Limit Theorem. Note: Remember that the Poisson distribution is a discrete distribution with PMF fx(x; A) х! where xe {0,1,2,3,……}, and 1 > 0 and hence E(X) = A , and Var(X) = A.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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