## Confidence Intervals

tsakanikasnickos on Thursday, November 27 2014, 03:51 PM
0
1. Let $$\displaystyle X_{1} , \dots X_{n}$$ be a random sample from a population with distribution $$\displaystyle Exp\left(\frac{1}{\theta}\right)$$, where $$\theta > 0$$. Find a confidence interval for $$\theta$$.
2. Let $$\displaystyle X_{1} , \dots X_{n}$$ be a random sample from a population with density

$\displaystyle f(x| \theta_{1},\theta_{2}) = \frac{\theta_{1}}{\theta_{2}} x^{\theta_{2}-1}{e}^{-\frac{x^{\theta_{2}}}{\theta_{1}}}$

where $$\theta_{1}>0,\theta_{2}>0,x>0$$ and $$\theta_{2}$$ is known. Find a confidence interval for $$\theta_{1}$$.

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