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Tim Yes there is: this is a trivial application of Bayes' theorem. Write down the likelihoods and you see that the distribution is bivariate normal (and with not much work you can write down the form). Mark Senior scientist Radiation Epidemiology Branch National Cancer Institute Executive Plaza South, 6120 Executive Boulevard MSC 7238 Rockville, MD 20852-7238 USA email [log in to unmask] email [log in to unmask] email [log in to unmask] website http://www1.imperial.ac.uk/med/people/mark.little.html tel: +1 301 594 7299 mobile: +1 301 875 3413 mobile: +44 7837798462 -----Original Message----- From: A UK-based worldwide e-mail broadcast system mailing list [mailto:[log in to unmask]] On Behalf Of Mak, Timothy Sent: 30 July 2010 13:47 To: [log in to unmask] Subject: A maybe simple maybe not so simple question on mathematical statistics Hi allstat list, Much appreciated if you could help me in this: Suppose Prior distribution for A and B are jointly normally distributed. C = A + B, so prior distribution for C is also normally distributed. Now suppose X is the data, and X ~ Normal(C, sigma^2) Suppose sigma^2 is known. Now posterior distribution of C is also normal. However, is there an analytic formula for the posterior distribution of A and B? Thanks in advance, Tim You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank. You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank.