Question
Suppose that $Y_{1}, Y_{2}, \ldots, Y_{n}$ constitute a random sample of size $n$ from an exponential distribution with mean $\theta$. Find a $100(1-\alpha) \%$ confidence interval for $t(\theta)=\theta^{2}$.
Step 1
The probability density function of an exponential distribution is given by $f(y;\theta) = \frac{1}{\theta}e^{-y/\theta}$. Therefore, the likelihood function for a sample of size $n$ is given by: \[L(\theta; Y) = \prod_{i=1}^{n} f(y_i;\theta) = \prod_{i=1}^{n} Show more…
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