A text file contains 1000 characters When the file is sent b

A text file contains 1000 characters. When the file is sent by e-mail from one machine to another, each character (independently of all other characters) has probability 0.001 of being corrupted. Use a Poisson random variable to estimate the probability that the file is transferred without error. Compare this to the answer obtained when you model the number of errors as a binomial random variable.

Solution

a)

Use a Poisson random variable to estimate the probability that the file is transferred without error.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes = n p = 1000*0.001 =    1      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.367879441 [ANSWER]

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b)

USING BINOMIAL:

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    1000      
p = the probability of a success =    0.001      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.367695425 [ANSWER]

As we can see, the results of parts A and B are very close to each other. [CONCLUSION]