MATH 340 Midterm: MATH 340 2006 Winter Test 2

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9 Jan 2019
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Be sure that this examination has 12 pages including this cover. Calculators, notes, or other aids may not be used. A note sheet is provided with the exam. You have two extra pages at the back for additional space. Rules governing examinations: each candidate should be prepared to produce his library/ams card upon request, read and observe the following rules: No candidate shall be permitted to enter the examination room after the expi- ration of one half hour, or to leave during the rst half hour of the examination. Candidates are not permitted to ask questions of the invigilators, except in cases of supposed errors or ambiguities in examination questions. The plea of accident or forgetfulness shall not be received: smoking is not permitted during examinations. [8: consider a zero sum game with m being player a"s payout matrix. (a) show that for any matrix m and probability vectors ~ , ~ (of appropriate dimen- sion) we have.