# Thread: Assume that the time of failure..

1. ## Assume that the time of failure..

Question : Assume that the time of failure, X of a telephone switching system follows exponential distribution with a failure rate $\lambda$.Estimate the maximum likelihood failure rate $\lambda$ from a random sample of n times to failure
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can any one provide me with the maximum failure rate of exponential distribution

2. Originally Posted by zorro
Question : Assume that the time of failure, X of a telephone switching system follows exponential distribution with a failure rate $\lambda$.Estimate the maximum likelihood failure rate $\lambda$ from a random sample of n times to failure
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can any one provide me with the maximum failure rate of exponential distribution
The question is simply asking you to find the maximum likelihood estimator of the parameter in an exponential distribution. How to do something like this has been explained in other threads started by you. Please use them as a guide to answering this question.

If you get stuck, please show ALL of your working and say where you are stuck.

3. $
\frac{d[ln \ L( \theta)]}{d \theta} = - \frac{n}{\theta}+\frac{1}{\theta^2} \sum_{i=1}^{n} x_i$

But after this i am stuck what should i do now??????

4. Originally Posted by zorro
$
\frac{d[ln \ L( \theta)]}{d \theta} = - \frac{n}{\theta}+\frac{1}{\theta^2} \sum_{i=1}^{n} x_i$

But after this i am stuck what should i do now??????
Do you understand what you're meant to do with the likelihood function? What does post #4 here: http://www.mathhelpforum.com/math-he...ival-rate.html

say you have to do.

You are meant to have done several of these (you have posted several). Go and review this material in your class notes or textbook.

By the way,
please show ALL of your working and say where you are stuck
does not mean show the final line of your working.

5. But that link which u provided is for poisson distribution and here we have to use exponential distribution how are they similar

6. Originally Posted by zorro
But that link which u provided is for poisson distribution and here we have to use exponential distribution how are they similar
The process of finding a maximum likelihood estimator is the same for all distributions. Do you understand this?

You are meant to learn from previous examples (experience) and apply what you have learned from them to the next problem.

7. Originally Posted by zorro
$
\frac{d[ln \ L( \theta)]}{d \theta} = - \frac{n}{\theta}+\frac{1}{\theta^2} \sum_{i=1}^{n} x_i$

But after this i am stuck what should i do now??????
calc 1, set equal to zero, zero