Suppose the lifespan of a Mayfly has exponential distribution with

parameter λ (indays). A child puts n them in a jar (with food and holes for air) and returns one daylater to find that r flies are dead.

 What is her maximum likelihood estimate for λ?

The girl is intrigued, so she repeats the experiment

. This time she stays up all day andall night, recording the exact times X1, . . . , Xr at which Mayflies die. (One supposesthis child is either the granddaughter of E. O. Wilson or deeply disturbed.)

 When shefinally falls asleep 24 hours later, n − r Mayflies are