Question: Suppose (x1, . . . , xn) is a random sample from an exponential distribution with mean 1/. 1. Derive the Jeffrey's prior for 2.

Suppose (x1, . . . , xn) is a random sample from an exponential distribution with mean 1/.

1. Derive the Jeffrey's prior for

2. Derive the posterior distribution of using the Jeffrey's prior.

3. Derive the predictive distribution of a future observation z.

4. Derive a 95% credible interval for z.

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