Question

4. A sample of size n-81 is taken from an exponential distribution with the pdf f(x)-Be-6x, θ > 0, x > 0. The sample mean is i-35. Find a 95% large- sample confidence interval for θ using the Central Limit Theorem.

Answer 1

here for above exponential distribution estimate mean =estimated std deviation =0.35=1/$\theta$

from above 95% confidence interval for mean " 0.274 <1/$\theta$ <0.426

or 1/0.426 <$\theta$ <1/0.274

or 2.346 <$\theta$<3.653