I'm now learning Bayesian inference.This is one of the questions I'm doing.
Suppose we have R.V.s $X_1,X_2,\ldots,X_n$ each have an Exponential distribution with parameter $\theta$. and prior for $\theta$ is an Exponential distribution with parameter $\lambda$. So what would you do to find posterior?
Attempts: Prior should be PDF of exponential with parameter $\lambda$. Likelihood should be product of PDF of exponential of each $X_i$, with parameter $\theta$.
Then what would you do next?