# find the probability that the compoent can last the mission

• Nov 30th 2011, 07:31 PM
wopashui
find the probability that the compoent can last the mission
Suppose that a critical component of an experiment to be performed on a space shuttle has an expected lifetime of 10 days which is exponentially distributed. As soon as a component fails, an identical component instantaneously takes its place. If the mission lasts 10 days and there are 2 spare components on board, what is the probability that these 3 components last long enough for the space shuttle to accomplish its mission?
Answer this question (i) using an appropriate continuous distribution, and (ii) using an appropriate discretedistribution.

for (i), I have use the exp(30) distribution to find the probability is 0.7165, but im kind of stuck with the diecrete one, i know it should be possion, but what is lamda, is it1/30?
• Dec 1st 2011, 12:19 AM
CaptainBlack
Re: find the probability that the compoent can last the mission
Quote:

Originally Posted by wopashui
Suppose that a critical component of an experiment to be performed on a space shuttle has an expected lifetime of 10 days which is exponentially distributed. As soon as a component fails, an identical component instantaneously takes its place. If the mission lasts 10 days and there are 2 spare components on board, what is the probability that these 3 components last long enough for the space shuttle to accomplish its mission?
Answer this question (i) using an appropriate continuous distribution, and (ii) using an appropriate discretedistribution.

for (i), I have use the exp(30) distribution to find the probability is 0.7165, but im kind of stuck with the diecrete one, i know it should be possion, but what is lamda, is it1/30?

The expected number of failures in a time window of length $\tau$ is $\tau/10$ (which in this case is 1), and the distribution of the number of failures has a Poisson distribution.

So you need to find the probability of 4 or more failures in a 10 day mission given the number of failures has a Poisson distribution with mean 1.

CB
• Dec 1st 2011, 11:23 AM
wopashui
Re: find the probability that the compoent can last the mission
Quote:

Originally Posted by CaptainBlack
The expected number of failures in a time window of length $\tau$ is $\tau/10$ (which in this case is 1), and the distribution of the number of failures has a Poisson distribution.

So you need to find the probability of 4 or more failures in a 10 day mission given the number of failures has a Poisson distribution with mean 1.

CB

sorry i make a mistake in part 1), let X=Y1+Y2+Y3, X has a gamma distribution with 3 and 10, we need to find P(X>=10), using the gamma pdf, but it's a function with the gamma function in it,which is gamma(3) I need to integrate it from 10 to infinity, i am not sure how to do it.