Please explain the solution to this? When 50 disk drives were tested in continuous use, 47 were still functioning perfectly after 200 days. If the lifetimes of the drives are assumed to have an exponential distribution, calculate the maximum likelihood estimate of the average lifetime.
Here we need to find the MLE of average lifetime of disk drives. And lifetimes follows exponential dist. with parameter, say lembda. But using the information given in qus, we can first use binomial likelihood of given sample. P is the prob. of a disk drive still functions after 200 days and one of the binomial parameters. Once we got the MLE of p, we can equate this prob. with prob. using exponential dist. which can be found simply integration the exponential pdf over limits 200 to ∞. It should be equal to p. So..we will got the MLE of lembda then (using invariance property of MLE) and hence the MLE of mean i.e.1/lembda which is required in qus.
