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Exponential Data Suppose you’re waiting for a bus that you think comes on average once every 10 minutes, but you’re not sure exactly how often it comes. $$ Y \sim Exp(\lambda) $$ Your waiting time has a prior expectation of $\frac{1}{\lambda}$ It turns out the gamma distribution is conjugate for an exponential likelihood. We need to specify a prior, or a particular gamma in this case. If we think that the buses come on average every ten minutes, that’s a rate of one over ten. $$ prior_{mean} = \frac{1}{10} $$ Thus, we’ll want to specify a gamma distribution so that the first parameter divded by the second parameter is $\frac{1}{10}$
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