3.15 Suppose data arose from an exponential distribution, with pdf f(x) = ex, for x 0 . We have a random sample of values:

3.15 Suppose data arose from an exponential distribution, with pdf f(x) = λe−λx, for x ≥ 0 .

We have a random sample of values: x1,...,xm, and further (n−m) values

(with n>m) which are right-censored at value τ. Thus the censored values are not known exactly — all we know is that they exceed τ in value. This is analogous to the censoring observed in Table 1.1, where the precise times to conception were not recorded for some individuals, only that they required greater than 12 cycles. Write down the likelihood for the data, and obtain the maximum-likelihood estimate of λ.