GATE 2022 ST – Question 33

Estimation · Point Estimation and Consistency · 1 mark · Numerical answer

Four observations 6,5,3,6 come from density 2(θ−x)/θ² on 0<x<θ,zero elsewhere. Find the method-of-moments estimate of θ as an integer.

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Correct answer: 15 to 15

Explanation

Integrating gives E X=(2/θ²)∫₀^θ x(θ−x)dx=θ/3. The sample mean is 20/4=5. Equate θ/3=5 to obtain **15**.

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