hw2_answer_econ120a_su06

hw2_answer_econ120a_su06 - Economics 120A Professor Yongil...

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Economics 120A Name: _________________________ Professor Yongil Jeon Summer 2006 Student ID#: _________________________ Answer to Homework #2 – Summer 2006 (Answer to Final Exam, Summer 2005) Answer all questions on separate paper. This problem set should be handed in to Professor Jeon at the beginning of your review session on Tuesday, August 1, 2006. Problem sets may not be handed in once solutions have been distributed. Please write down your name and PID clearly. Good luck! 1-a) (3 points) The Student t distribution is a. the distribution of the sum of m squared independent standard normal random variables. b. the distribution of a random variable with a chi-squared distribution with m degrees of freedom, divided by m . c. always well approximated by the standard normal distribution. d. the distribution of the ratio of a standard normal random variable, divided by the square root of an independently distributed chi-squared random variable with m degrees of freedom divided by m . Answer : d 1-b) (3 points) When there are degrees of freedom (that is, with a large sample), the t distribution a. can no longer be calculated. b. equals the standard normal distribution. c. has a bell shape similar to that of the normal distribution, but with “fatter” tails. d. equals the 2 χ distribution. Answer : b 1-c) (3 points) The central limit theorem a. states conditions under which a variable involving the sum of 1 ,..., n YY i.i.d. variables becomes the standard normal distribution. b. postulates that the sample mean Y is a consistent estimator of the population mean Y µ . c. only holds in the presence of the law of large numbers. d. states conditions under which a variable involving the sum of 1 ,..., n i.i.d. variables becomes the Student t distribution. Answer : a
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2 HOMEWORK #2, ECON 120A, Summer 2006 1-d) (3 points) The sample average is a random variable and a. is a single number and as a result cannot have a distribution. b. has a probability distribution called its sampling distribution. c. has a probability distribution called the standard normal distribution. d. has a probability distribution that is the same as for the 1 ,..., n YY i.i.d. variables. Answer : b 1-e) (3 points) An estimator ˆ Y µ of the population value Y is more efficient when compared to another estimator Y % , if a. E ( ˆ Y ) > E ( Y % ). b. it has a smaller variance. c. its c.d.f. is flatter than that of the other estimator. d. both estimators are unbiased, and var( ˆ Y ) < var( Y % ).
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hw2_answer_econ120a_su06 - Economics 120A Professor Yongil...

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