The lifetime, Y, of a certain type of component is known to follow the Exponential distribution. So for a sample of n such components, we know that the maximum likelihood estimator for Theta is Theta^= Y bar. The reliability of a component at a certain time t is defined to be r(t)=P(Y>t). For fixed t, find the maximum likelihood estimator for r(t).

I'm assuming r(t) should be replaced by 1-F(Y) but I really don't understand the maximum likelihood estimator method. I can't figure out how to start.