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July 24, 2022

Suppose the lifespan of a Mayfly has exponential distribution with parameter λ

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 still alive. What is the maximumlikelihood estimate of λ?

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