Consider the following statements: I. If Xi sim U(0, theta), theta in (0, infty), then max(X1, X2, X3, …, Xn) is sufficient for theta. II. If Xi sim ftheta(x) = begincases 1, & theta-0cdot 5 < x < theta+0cdot 5 0, & otherwise endcases, then (min Xi, max Xi) is jointly sufficient for parameter theta. Which of the statements given above is/are correct?

Q28Section I (Objective (Q1–Q80))28 of 80

Statistical Inference — sufficiency in two uniform families

Consider the following statements: I. If $X_i \sim U(0, \theta)$ , $\theta \in (0, \infty)$ , then $\max(X_1, X_2, X_3, …, X_n)$ is sufficient for $\theta$ . II. If $X_i \sim f_\theta(x) = \begin{cases} 1, & \theta-0\cdot 5 < x < \theta+0\cdot 5 \ 0, & \text{otherwise} \end{cases}$ , then $(\min X_i, \max X_i)$ is jointly sufficient for parameter $\theta$ . Which of the statements given above is/are correct?

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