Let x1 = 3, x2 = 4, x3 = 3cdot 5, x4 = 2cdot 5 be four observations from a distribution with pdf f(x mid theta) = 1/3[1/thetae^-x/theta + 1/theta^2e^-x/theta^2 + e^-x]; theta 0. The method of moment estimator of theta based on above observations is:

Q30Section I (Objective (Q1–Q80))30 of 80

Statistical Inference — moment estimator for a mixture

Let $x_1 = 3$ , $x_2 = 4$ , $x_3 = 3\cdot 5$ , $x_4 = 2\cdot 5$ be four observations from a distribution with pdf $f(x \mid \theta) = \frac{1}{3}\left[\frac{1}{\theta}e^{-\frac{x}{\theta}} + \frac{1}{\theta^2}e^{-\frac{x}{\theta^2}} + e^{-x}\right]$ ; $\theta > 0$ . The method of moment estimator of $\theta$ based on above observations is:

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