3
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.