Let x1,x2,dots,xn be a random sample from the distribution having p.d.f. f(x,theta)=e^-(x-theta); xtheta. Further, l(x(1)-log40/n,,x(1)r) is 100beta% confidence interval for theta, where x(1)=minx1,dots,xn. What is the value of beta?

Q5Section I (Objective (Q1–Q80))5 of 80

Confidence interval from the minimum of an exponential sample

Let $x_1,x_2,\dots,x_n$ be a random sample from the distribution having p.d.f. $f(x,\theta)=e^{-(x-\theta)}; x>\theta$ . Further, $\Bigl(x_{(1)}-\dfrac{\log40}{n},\,x_{(1)}\Bigr)$ is $100\beta\%$ confidence interval for $\theta$ , where $x_{(1)}=\min\{x_1,\dots,x_n\}$ . What is the value of $\beta$ ?

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