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If $x_1$ and $x_2$ are the values of random sample of size $n=2$ from a population having a uniform distribution with parameters $0$ and $\theta>0$, find the number $k$ so that the interval $[0, k(x_1+x_2)]$ is a $(1-\alpha)100\%$ confidence interval for the parameter $\theta$ when (1) $\alpha\leq 1/2$; and (2) $\alpha>0$.

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is the joint density 1/theta^2? i do not know how to find the bound of the double integral.. – Dan Mar 13 '13 at 18:08
And i feel i do not understand this question so well. Does alpha need to be greater than 0 spontaneously? – Dan Mar 13 '13 at 18:15

You need to determine the distribution of $X_1 + X_2$ in function of $\theta$. Then calculate $k_\alpha$ such that $$ \mathbb P ( k_\alpha (X_1+ X_2) \geq \theta) = 1-\alpha. $$

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Thx! I mean... how to calculate the integral and what is the bound? – Dan Mar 14 '13 at 0:12

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