Suppose that 1 , , Yn are independent and identically distributed on the interval , +

Suppose that Υ1

, …, Yn are independent and identically distributed on the interval

θ, θ + 1. Show that the likelihood function is constant in the interval (y(n) − 1, y(1)

)

and is zero otherwise. Hence, interpret r = y(n) − y(1) as an indicator of the shape of the likelihood function.

Financial support for this research was provided in part by NSF Grants No. DMS8404941 and DMS-8601732.