ProblemSet1

# ProblemSet1 - Econ 103 UCLA Fall 2010 Problem Set 1 Due...

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Unformatted text preview: Econ 103 UCLA, Fall 2010 Problem Set 1 Due: Thursday, October 7 in hardcopy at the beginning of class Note: Please attach the “Homework Cover Page” from Classweb to the front of your home- work. Part 1: True or False and explain briefly why. 1. The expected value of a discrete random variable is the outcome that is most likely to occur. 2. If two random variables X and Y are independently distributed, then E ( Y ) = E ( Y | X ) . 3. A probability density function tells the probability that a random variable is less than or equal to a certain value. 4. V ar ( X + Y ) = V ar ( X ) + V ar ( Y ) + 2 Cov ( X,Y ) 5. V ar ( X- Y ) = V ar ( X )- V ar ( Y )- 2 Cov ( X,Y ) 6. If ρ XY = 0 , then X and Y are independent. 7. Let Y be a random variable. Then the standard deviation of Y equals E ( Y- μ Y ) . 8. Assume that X , Y , and Z follow the distribution N ( μ,σ 2 ) . Then W = X + Y- Z is normally distributed. 9. Assume that Y ∼ F 1 , ∞ . Then Y ∼ χ 2 1 . 10. Observations in a random sample are independent of each other. 11. If ˆ μ is an unbiased estimator of μ , then ˆ μ = μ . 12. If the p-value equals . 96 , then we cannot reject the null hypothesis. 13. The standard error of ¯ Y equals the standard deviation of Y . That is, SE ( ¯ Y ) = σ Y . 14. Assume that H : μ Y = μ Y, and H 1 : μ Y > μ Y, , and Y is normally distributed. To compute the critical value for this 1-sided test, we divide by two the positive critical value of the 2-sided test. 15. Everything else equal, the length of the confidence interval decreases with the sample size n ....
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ProblemSet1 - Econ 103 UCLA Fall 2010 Problem Set 1 Due...

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