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Let Xi ∼ Poi(1), i = 1, . . . , n, be n = 20 independent Poisson r.v’s.

Let Xi ∼ Poi(1), i = 1, . . . , n, be n = 20 independent Poisson r.v’s.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3. Let Xi ∼ Poi(1), i = 1, . . . , n, be n = 20 independent Poisson r.v’s.
Hint: you may use E(Y ) = λ and Var(Y ) = λ, for a Poisson r.v. Y ∼ Poi(λ).

3a. Use the Markov inequality to obtain a bound on Pr (Ln Xi > 30) (±0.05 is okay).

3b. Use the CLT to approximate the same probability (±0.01 is okay)

3. Let X; Poi(1), i = 1, ..., n, be n = 20 independent Poisson r.v's. Hint: you may use E(Y)= \ and Var(Y) = \, for a Poisson r.v. Y ~ Poi(A). 3a. Use the Markov inequality to obtain a bound on Pr (- X; > 30) (±0.05 is okay). Pr (E1 X; > 30) < i=1 3b. Use the CLT to approximate the same probability (+0.01 is okay) Pr (E1 X; > 30) = i=1
Transcribed Image Text:3. Let X; Poi(1), i = 1, ..., n, be n = 20 independent Poisson r.v's. Hint: you may use E(Y)= \ and Var(Y) = \, for a Poisson r.v. Y ~ Poi(A). 3a. Use the Markov inequality to obtain a bound on Pr (- X; > 30) (±0.05 is okay). Pr (E1 X; > 30) < i=1 3b. Use the CLT to approximate the same probability (+0.01 is okay) Pr (E1 X; > 30) = i=1
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