Ill assume the lifetime of each machine is independant of the others.
I think Lambda is 1/beta. in any case, just use the CDF as you ahve been taught it.
say i have three machines connected in parallel. the life expectancy of each machine is exponentially distributed with beta value of 10. The system is in the working state if any one of the connected component is working.
Find the probability of the system operating for more than 5 hours.
i heard that to apply order statistics the distributions should be the same now if the beta values are different then the distributions will not be the same. Am i correct
So in this case you cannot apply order statistics principles you have to go in the general way
am i correct?
no i did not mean for binomial distribution.
X1 - distribution of macine 1
X2 - distribution of machine 2
X3- distribution of machine 3
each machine's life is exponentially distributed.
But since each machine's beta values are not the same order stat principles cannot be applied in this case. Am i correct ?