Economics 120A Name: _________________________ Professor Yongil Jeon Winter 2008 Student ID#: _________________________ Answer to Homework #1 – Winter 2008 (Part of Midterm Exam, Summer 2007) 1. True/False (4 points each) 1.The optimal solution to a mathematical model is always the policy that should be implemented by the company. Answer: False 2.Microcomputers have made most quantitative approaches to decision making more accessible to even moderate size firms. Answer: True 3.Past data might be used to test the validity of a mathematical model. Answer: True 4.Pr(A|B)=1 – Pr(B|A) for all events A and B. Answer: False 5.If A and B are mutually exclusive, Pr(A) + Pr(B) must equal 1. Answer: False 2. (10 points). Prove that the averageof deviations about the sample mean is zero. Answer: The question asks you to show that for sample size n, that the averageof deviations about the sample mean is zero: Using the definition of the sample mean, this can easily be shown: ()110.niinXX=−=∑()1111110.nnniiiiinnnnnXXXXXX===⎡⎤⎡⎤−=−=−=⎢⎥⎣⎦⎣⎦∑∑∑
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