Q8Section I (Objective (Q1–Q80))8 of 80

Statistical Inference — range statistic in uniform location family

Let $X_1, X_2, X_3, …, X_n$ be a random sample of size $n$ taken from $U(\theta - 0\cdot 5, \theta + 0\cdot 5)$ where $\theta \in (-\infty, \infty)$ . If $T_1$ and $T_2$ are respectively the minimum and maximum order statistics, then which of the following statements is/are correct regarding the statistic $T = T_2 - T_1$ ? I. $T$ is sufficient statistic of $\theta$ . II. $T$ has a complete family of distributions. Select the answer using the code given below:

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