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Unformatted text preview: Econ 103 UCLA, Spring 2011 Problem Set 1 Due: Tuesday, April 12 in hardcopy at the beginning of class Note: Please attach the Homework Cover Page , which you can download from the class website, to the front of your homework. Part 1: True or False and explain brie y 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. Observations in a random sample are independent of each other. 10. If ˆ μ is an unbiased estimator of μ , then ˆ μ = μ . 11. If the pvalue equals . 96 , then we cannot reject the null hypothesis. 12. The standard error of ¯ Y equals the standard deviation of Y . That is, SE ( ¯ Y ) = σ Y . 13. 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 1sided test, we divide by two the positive critical value of the 2sided test. 14. Everything else equal, the length of the con dence interval decreases with the sample size n ....
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 Spring '07
 SandraBlack
 Normal Distribution, Standard Deviation, Variance, Probability theory

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