GATE 2025 ST – Question 32
Observed Bernoulli sample values are 0,1,1,1,0, with parameter θ∈(0,.7]. Find the MLE of θ to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.59 to 0.61
Explanation
The likelihood is θ³(1−θ)². Its log derivative 3/θ−2/(1−θ)=0 gives θ=3/5=.6, inside the parameter interval. The log likelihood is strictly concave, so the maximum is **.60**.