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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 XY = 0 , then X and Y are independent. 7. Let Y be a random variable. Then the standard deviation of Y equals E ( Y- Y ) . 8. Assume that X , Y , and Z follow the distribution N ( , 2 ) . Then W = X + Y- Z is normally distributed. 9. Observations in a random sample are independent of each other. 10. If is an unbiased estimator of , then = . 11. If the p-value 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 ) = Y . 13. Assume that H : Y = Y, and H 1 : Y > 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. 14. Everything else equal, the length of the con dence interval decreases with the sample size n ....
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