A Unit Window of Unknown Position
A sample 2.3, 2.9, 2.6 is drawn from the Uniform(θ, θ+1) distribution, with θ unknown. The set of values of θ that maximize the likelihood is an interval. What is its length? Give an exact fraction or a decimal.
Related problems & prerequisites
Worth solving first
Source: Standard example of non-unique maximum likelihood estimators. Statement written for AxiomIQ.