Let X1, X2, X3 be a random sample from a distribution having probability mass function ftheta(x) = begincases theta, & x = 1 1 - theta, & x = 2 0, & otherwise endcases, where theta in Theta = (0, 1). Let X = (X1, X2, X3). Then which of the following is NOT a sufficient statistic for theta?

(B) T2(X) = (X1 + X2,; X1 - X3,; X2 + X3)

Q43Section ST (Statistics (Q11–Q65))43 of 65

Sufficiency of sample statistics

Let $X_1, X_2, X_3$ be a random sample from a distribution having probability mass function $f_\theta(x) = \begin{cases} \theta, & x = 1 \ 1 - \theta, & x = 2 \ 0, & \text{otherwise} \end{cases}$ , where $\theta \in \Theta = (0, 1)$ . Let $X = (X_1, X_2, X_3)$ . Then which of the following is NOT a sufficient statistic for $\theta$ ?

Pick an option to check your answer. In a mock test a wrong answer here costs 2/3 mark.

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