"A factory contains 8 machines. These machines can break down independently of the other machines following an exponential distribution with a mean value of 10 years.
What is the distribution of time until all 8 machines break down?"
I understand that the lambda in this situation is 1/10, but the fact that the question is looking for a distribution of time is what is throwing me. Am I correct in thinking that I will be using 8*(1/10) or 8/10 as my lambda for this distribution because it involves all 8 independent machines?
Would that mean that:
[MATH]f(x) =0.8 e^{-0.8x}[/MATH]? This is the time between 8 blowouts right? And is it therefore what the question is asking for? Or should I be looking at the Cumulative density function and working at when the probability =1?
Sorry that I'm unable to fully explain my line of thinking, the fact that it isn't actually asking for a numerical answer and instead a distribution is confusing to me. Any help is greatly appreciated, thanks.
What is the distribution of time until all 8 machines break down?"
I understand that the lambda in this situation is 1/10, but the fact that the question is looking for a distribution of time is what is throwing me. Am I correct in thinking that I will be using 8*(1/10) or 8/10 as my lambda for this distribution because it involves all 8 independent machines?
Would that mean that:
[MATH]f(x) =0.8 e^{-0.8x}[/MATH]? This is the time between 8 blowouts right? And is it therefore what the question is asking for? Or should I be looking at the Cumulative density function and working at when the probability =1?
Sorry that I'm unable to fully explain my line of thinking, the fact that it isn't actually asking for a numerical answer and instead a distribution is confusing to me. Any help is greatly appreciated, thanks.