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statsexam2f11sol_1

# statsexam2f11sol_1 - Economic Statistics Exam 2 Last name...

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Economic Statistics Exam 2 Last name: November 3, 2011 First name: Class time: SOLUTIONS PID: Please sign that you abide by the honor pledge: This exam contains twelve short answer questions (worth 6 points each) and three long answer questions (worth 10 points each). Please answer in the space provided. In all problems where you need to make a calculation, simplify your answer as much as possible. Technique is important, so show your work clearly. Some PDFs: Some probabilities: f ( x ) = 1 2 πσ 2 e ( X μ ) 2 2 σ 2 P [ x a ] = 1 e λ a f ( x ) = 1 u P [ x ] = x e x ! f ( x ) = e x P [ x ] = n ! x !( n x )! p x (1 p ) n x 1. For a binomial distribution with p = 0.7 and n = 50 , what is the expected value of x , and what is the variance in x ? E [ x ] = n p = 50 0.7 = 35 Var ( x ) = n p (1 p ) = 50 0.7 0.3 2. In the entire population, x is distributed normally with a mean of 5.28 and a standard deviation of 8.26. If a researcher calculates the mean of a random sample of n = 25 , then what is the distribution of his/her sample mean, x ? x ~ N ( x , x 2 / n ) , which is x ~ N (5.28,8.26/25) .

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Econ 400 Midterm 2, page 2 of 6. 3. X ~ N (1,9) . You collect a sample of n = 25 . What is the probability that X > 3 ? X has a mean of 1 and standard deviation of 9 25 = . P [ X > 3] = P [ Z > (3 1)/(3/5)] = P [ Z > 10/3] = P [ Z > 3.33] . Depending on the z-table you use, the answer is either “0.0004” or “less than 0.5000-0.4990” or “approximately 0.0000”. 4. Two random variables, x and y , have a joint distribution. What is the formula for calculating the covariance between the random variables?
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statsexam2f11sol_1 - Economic Statistics Exam 2 Last name...

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