GATE 2020 ST – Question 35
Observed data0,1,2,3 come from N(θ,5), with θ restricted to[2,∞). Find the maximum-likelihood estimate.
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Correct answer: 2 to 2
Explanation
With known variance, maximizing likelihood minimizesΣ(xi−θ)². The unrestricted minimizer is sample mean1.5, outside the allowed parameter set. The nearest admissible value is its boundary2; likelihood decreases for θ>2. Thus the constrained MLE is2.