The lifetime of a certain component may be modelled by the exponential distribution with probability density function: f(t) = lambda*exp^(-lambda*t).

In a test, n items were used, m items failed, having times to failure t1, t2,..., tm.

The remaining items were still working when the test was terminated at time t0.

Show that the maximum likelihood estimate for lambda is lamdba = m /(sum of ti + (n-m)*t0)?

Any help is appreciated!