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34 A career in statisticsBruno de Finetti heard of this method and he wrote to me suggestingthat the student should be encouraged to state their probability for each ofthe possible choices. The appropriate score should be a simple function ofthe probability distribution and the correct answer. An appropriate functionwould encourage students to reply with their actual distribution rather thanattempt to bluff. I responded that it would be difficult to get third graders tolist probabilities. He answered that we should give the students five gold starsand let them distribute the stars among the possible answers.3.3 University of Illinois and StanfordIn 1949, Arrow and Rubin went to Stanford, and I went to the MathematicsDepartment of the University of Illinois at Urbana. During my second year atUrbana, I received a call from Arrow suggesting that I visit the young StatisticsDepartment at Stanford for the summer and the first quarter of 1951. Thatoffer was attractive because I had spent the previous summer, supplementingmy $4,500 annual salary with a stint at the Operations Research Office ofJohns Hopkins located at Fort Lesley J. McNair in Washington, DC. I hadenjoyed the visit there, and learned about the Liapounoff theorem about the(convex) range of a vector measure, a powerful theorem that I had occasion tomake use of and generalize slightly (Chernoff, 1951). I needed some summersalary. The opportunity to visit Stanford with my child and pregnant wife wasattractive.The head of the department was A. Bowker, a protégé oftheprovostF. Terman. Terman was a radio engineer, returned from working on radar inCambridge, MA during the war, where he had learned about the advantagesof having contracts with US Government agencies and had planned to exploitsuch opportunities. Essentially, he was the father of Silicon Valley. The StatisticsDepartment had an applied contract with the Office of Naval Research(ONR) and I discovered, shortly after arriving, that as part of the contract,the personnel of the department supported by that contract were expectedto engage in research with relevance to the ONR and to address problemsposed to them on annual visits by scientists from the NSA. We distributedthe problems posed in mathematical form without much background. I wasgiven the problem of how best to decide between two alternative distributionsof a random variable X when the test statistic must be a sum of integers Ywith 1 ≤ Y ≤ k for some specified value of k and Y must be some unspecifiedfunction of X. It was clear that the problem involves partitioning the space ofX into k subsets and applying the likelihood ratio. The Liapounoff theoremwas relevant and the Central Limit Theorem gave error probabilities to useto select the best procedure.