I am working on this question:

A text file contains 6000 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.

My solution so far:

  • $N = 6000$ since there are 6000 trials

  • the probability of success of each trial (of not being corrupted) is $1-0.001=0.999$

  • Let X be the random variable that represents the number of sucesses

So I use the Poission distribution formula: $$P\{X = k\} = \frac{e^{-\lambda}\lambda^k}{k!}$$

So I want to find the probability of 6000 successes, which means that the file transferred successfully without any errors: $$\lambda = N\cdot p = 6000(0.999)=5994$$ $$P\{X = 6000\} = \frac{e^{-5994}(5994)^{6000}}{6000!}$$

However this number cant be calculated by my calculator so I assuming that I have did something wrong. But all my working out makes sense so far so I don't know where I have gone wrong.


Hint: It's a lot easier to calculate the probability of 0 failures instead of 6,000 successes.

  • $\begingroup$ Is the probability of 0 errors equivalent to the probability of 6000 successes of no errors? $\endgroup$ – karambit Jan 30 '16 at 15:34
  • $\begingroup$ @katambit, yes it is. $\endgroup$ – Paul Jan 30 '16 at 15:35

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