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## Homework Statement

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.

## Homework Equations

p_x(k) = (a^k)(e^-a)/(k!), poisson

p_x(k) = (n choose k)(p^k)(q^{n-k}), binomial

## The Attempt at a Solution

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:

E(x) = np = 1000 x 0.001 = 1

I don't really think I'm tackling either of these problems in the correct way but don't know what else to do. Thanks for any help.