First let me say I am not a student asking for homework help. I have been perusing a old book of mine 'Introduction to the Theory of Statistics' (Mood 1950) and have come across the following problem at the end of one of the chapters. It is stated exactly as follows:"Suppose intelligence quotients for students in a particular age group are normally distruibuted about a mean of 100 with standard deviation of 15. The I.Q.,say x , of a particular student is to be estimated by a test on which he scores 130. It is further given that test scores are normally distributed about the true I.Q. as a mean with standard deviation 5. What is the maximum-likelihood estimate of the student's I.Q.? (The answer is not 130)." Unless the answer is 110, I am clueless
This was originally posted under "homework help", which I thought I explained right in the beginning that it was not. I had hoped that Galactus would comment.

From what I can gather, this problem is rather complicated and is famous in the stats world in regards to Henderson(a famous and ingenious statistician). Here is a link telling a little about it. Scroll down to page 6:

http://jds.fass.org/cgi/reprint/74/11/4035.pdf

Galactus: I went to the link you suggested and sure enough there was the problem, quoted exactly. I also noted that in the list of references was A. M. Mood's "Introduction to the Theory of Statistics" Makes me wonder, which came first, the chicken or the egg? Mood hadn't introduced matrices before the problem was asked, so Henderson's work didn't help me. However, I appreciate your comments and salute your what appears to be an excellent memory for details. If you happen to work on the problem further and come up with an answer I would appreciate hearing from you. Thanks for your effort.