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# HW2 - Problem Set 2 Due Tuesday Econ 319 Introduction to...

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Problem Set 2 - Due Tuesday 09/23/08 Econ 319 - Introduction to Probability and Statistics Fall 2008 Cornell University Prof. Molinari This was Test 1 for this class during one of the semesters in which I taught it. As you will see, the exam consisted of TWO parts totaling 100 points. I will maintain the same structure for the Test 1 that I am preparing for your class. The exam will be a CLOSED BOOK exam. However, useful formulas will be provided on pages 4+. Calculators are permitted °but graphic calculators are prohibited. You will have 75 minutes to complete the exam. SHOW ALL your work as partial credit will be given. Answers without explanations might NOT be given (full) credit even if they are correct. Part 1 ° 25 points (5 points each) In WORDS , brie±y (1 paragraph maximum) describe the following: 1. Sample Space. 2. Independence of two events. 3. Independence of two random variables. 4. Conditional Probability. 5. Expected Value. 1

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Part 2 ° 75 points (Each sub-question has the number of corresponding points in brackets) 1. Given three events A , B and C; is Pr ( A j B \ C ) + Pr ( A 0 j B \ C ) = 1? If your answer is yes, give a proof; if your answer is no, give a counterexample. Is Pr ( A j B \ C )+Pr ( A j B 0 [ C 0 ) = 1? If your answer is yes, give a proof; if your answer is no, give a counterexample. (5 points) 2. Suppose Cornell²s rowing team has a group of four scullers (i.e., rowers who row each with two oars), being considered to form the Quadruple in the U.S. National Rowing Team. The coach of the National Team has decided to test the athletes on how fast each of them can complete a 2,000 meter distance alone, on a so called ³single boat.´Each of the four athletes² performance on the test is independent of the others. Let
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HW2 - Problem Set 2 Due Tuesday Econ 319 Introduction to...

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