A text file contains 1000 characters. When the file is sent by email from one machine to another, each character (independent of other characters) has probability 0.001 of being corrupted. Use a poisson random variable to estimate the probability that the file is transferred with no errors. Compare this to the answer you get when modelling the number of errors as a binomial random variable.(adsbygoogle = window.adsbygoogle || []).push({});

Poisson:

Let x be the number of corrupted characters.

E(X) = 0.001 = a

P(X=n) = (0.001^n)(e^-0.001)/(n!)

P(X=0) = e^-0.001

Binomial:

np = 1000 x 0.001 = 1

When I approximate using poisson but with np instead I get e^-1 which is about 0.37.

This doesn't seem right?

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# Homework Help: Poisson and binomial distributions, corrupted characters in a file

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