Q21Comprehension2 Marks1 Sep 2024PassageBased on the above data, answer the given subquestions. Let X1,X2,…,X50X_1, X_2, \ldots, X_{50}X1,X2,…,X50 be i.i.d. samples from Uniform(θ,2θ)\text{Uniform}(\theta, 2\theta)Uniform(θ,2θ) distribution, where θ>0\theta > 0θ>0.Find the method of moments estimator of θ\thetaθ.Aθ^MME=32(X1+…+X5050)\hat{\theta}_{MME} = \frac{3}{2}\left(\frac{X_1 + \ldots + X_{50}}{50}\right)θ^MME=23(50X1+…+X50)Bθ^MME=X1+…+X5050\hat{\theta}_{MME} = \frac{X_1 + \ldots + X_{50}}{50}θ^MME=50X1+…+X50Cθ^MME=23(X1+…+X5050)\hat{\theta}_{MME} = \frac{2}{3}\left(\frac{X_1 + \ldots + X_{50}}{50}\right)θ^MME=32(50X1+…+X50)Dθ^MME=2(X1+…+X5050)\hat{\theta}_{MME} = 2\left(\frac{X_1 + \ldots + X_{50}}{50}\right)θ^MME=2(50X1+…+X50)
