A random sample of size m from N(0, 2), with known and having a uniform prior distribution, yields a sample mean x. Show that the distribution of the mean from a second independent random sample of size n from the same distribution, given the value of x; that is, p(x,); is N(x, (m+n-)). A scientist using an apparatus of known standard deviation 0-12 takes nine independent measurements of the same quantity and obtains a mean of 17-653. Obtain limits between which a tenth measurement will lie with 99% probability.