Let X1, · · · , X20 be independent Poisson random variables with mean (print please)...
Let X1, · · · , X20 be independent Poisson random variables with mean (print please)
1. (i) Use the pmf of Poisson distribution to compute P(X1 + · · · + X20 > 15).
(ii) Use the Markov inequality to obtain a bound on P(X1 + · · · + X20 > 15).
(iii) Use the central limit theorem to approximate P(X1 + · · · + X20 > 15).
Homework Answers
Assuming lambda = 1
i)
Y = X1+X2+...+X20
Y follow poisson (20* lambda) = Pois(20)
P(Y > 15)
= 1- P(Y <= 15)
= 1- poisson.dist(15,20,1)
=
| 0.843487 |
ii) and iii)
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Let X1, · · · , X20 be independent Poisson random variables with
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