Let x1,x2,dots,xn be a random sample from the following probability distribution: P(X=1)=2(1-theta)/2-theta,qquad P(X=2)=theta/2-theta;qquad thetain(0,1). The moment estimate of theta is:

Q7Section I (Objective (Q1–Q80))7 of 80

Method of moments estimator

Let $x_1,x_2,\dots,x_n$ be a random sample from the following probability distribution:

$\mathbb{P}(X=1)=\frac{2(1-\theta)}{2-\theta},\qquad \mathbb{P}(X=2)=\frac{\theta}{2-\theta};\qquad \theta\in(0,1).$

The moment estimate of $\theta$ is:

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