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Suppose the life of a computer can be modeled with an exponential random variable with parameter $\lambda$=(1/10) aka, .1 computers crash per year. How would I find the probability that exactly 14 crashes will occur in a month?

So, I think that lambda = $\frac1{120}$ crashes per month and I think I need to find Pr(X=14). Based on the top answer from this question, I think I'm calculating:

$$ P_{14}(t) = \frac{(\frac1{120} *1)^{14}}{14!} e^{\frac1{120} *1}$$

(since t = 1 month, assuming there are 30 days in a month)

But I'm not quite sure that I'm doing this correctly.

nodel
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    The number of crashes is not exponentially distributed. I think you are trying to say that the time between crashes is exponential or the number of crashes per fixed time models a Poisson distribution. Note that both of those statements are equivalent. – Cliff AB Jun 10 '17 at 00:55
  • I updated it to mean the computer's lifetime. – nodel Jun 10 '17 at 01:00
  • It looks right to me. – callculus42 Jun 10 '17 at 01:37
  • I guess I'm kind of confused when to use that equation and when to use the (exp(-lambda)*lambda^x) / x! equation.

    Tell me if I'm wrong, but let's say that I want to compare the probability of no computer crashes in a year vs month. For this, I used the second equation and got exp^(-1/10) and exp(-1/120) for year/month.

     – nodel Jun 10 '17 at 01:41
  • @nodel It is correct as well. – callculus42 Jun 10 '17 at 16:19

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