Let X1, X2 be a random sample from the following probability density function falpha(x) = begincases alpha x^alpha-1 e^-x^alpha, & x 0 0, & otherwise endcases, where alpha in (0, infty) is an unknown parameter. Let X(1) = minX1, X2 and X(2) = maxX1, X2. Then which of the following statements is correct?

(A) (X1 + X2,; X(1)) is a minimal sufficient statistic

Q19Section ST (Statistics (Q11–Q65))19 of 65

Minimal sufficient statistic for a Weibull shape

Let $X_1, X_2$ be a random sample from the following probability density function $f_\alpha(x) = \begin{cases} \alpha x^{\alpha-1} e^{-x^\alpha}, & x > 0 \ 0, & \text{otherwise} \end{cases}$ , where $\alpha \in (0, \infty)$ is an unknown parameter. Let $X_{(1)} = \min\{X_1, X_2\}$ and $X_{(2)} = \max\{X_1, X_2\}$ . Then which of the following statements is correct?

Pick an option to check your answer. In a mock test a wrong answer here costs 1/3 mark.

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