Given these assumptions, show that the prior probability distribution of dn is (mnemonic: when Gaussians multiply, precisions add). To start with, let"s evaluate the expected utility if we do no...

Given these assumptions, show that the prior probability distribution of dn is

(mnemonic: when Gaussians multiply, precisions add).

To start with, let"s evaluate the expected utility if we do no prospecting (i.e., choose the site immediately); then we"ll evaluate the expected utility if we first prospect at one site and then make our choice. From these two results we will be able to decide whether to prospect once or zero times, and, if we prospect once, at which site. So, first we consider the expected utility without any prospecting.