GATE 2026 ST – Question 32
A gamma sample has density λ^αx^(α−1)e^(−λx)/Γ(α),x>0, with unknown α,λ>0. The observed averages of x_i and x_i² are 2 and 5. Find the method-of-moments estimate of α (integer).
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Correct answer: 4 to 4
Explanation
The empirical variance for moment matching is 5−2²=1. Gamma moments give mean α/λ=2 and variance α/λ²=1. Their ratio gives λ=2, hence α=4. **4**.