Problem Set 1 Solutions

Problem Set 1 Solutions - Problem Set 1 Economics 103...

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1 Problem Set 1 Economics 103 Winter 2009 Due: Tuesday, January 20 Beginning of class Question 1: True, False, Explain. You are graded on your explanation. 1. The probability of an outcome is the number of times that the outcome occurs in the long run. False, the probability of an outcome is the number of times that the outcome occurs divided by the total number of outcomes 2. The expected value of a discrete random variable is the outcome that is most likely to occur. False, the expected value is the weighted average of the possible outcomes. 3. Let Y be a random variable. Then var( Y ) equals [( )] Y EY μ . False, var(Y) = E[(Y- μ y ) 2 ] 4. Two random variables X and Y are independently distributed if () [( | ) ] EEY X = . False—It is true that IF the variables are independent, THEN E(Y) = E(Y|X) but the implication does not go the other way. 5. The correlation between X and Y cannot be negative since variances are always positive. False, Corr(X,Y) = Cov(X,Y)/Sd(X)Sd(Y). If the covariance between X and Y is negative, then the correlation is negative. The correlation can range from -1 to +1. 6. To standardize a variable you add and subtract 1.96 times the standard deviation to the variable. False, to standardize a variable, you subtract its mean and divide by its standard deviation 7. Assume that Y is normally distributed 2 (, ) N μσ . Moving from the mean ( ) 1.64 standard deviations to the left and 1.64 standard deviations to the right, then the area under the
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2 normal p.d.f. is 0.05. False, P(-1.64<z<1.64) =.90 8. The sample average is a random variable and has a probability distribution that is the same as for the 1 ,..., n YY i.i.d. variables. False, the variance of the sample average is the variance of the iid variables divided by n, so the probability distributions are not the same. 9. If two random variables have a correlation of zero, they are independent. False, if two variables are independent, then they have a correlation of zero. 10. A probability density function tells the probability that a random variable is less than or equal to a certain value. False, a cumulative density function tells the probability that a random variable is less than or equal to a certain value. A pdf tells you the probability it is equal to a particular value (or, in the continuous case, within a small range.) 11. Econometric techniques allow us to establish a causal relationship between two variables. False, econometric techniques allow us to establish a correlation between two variables, the causal relationship is an assumption of the economic model. 12. An estimate and an estimator are the same thing. False, an estimator is a function of the data, an estimate is a specific value. 13. Any linear combination of normally distributed random variables is F-distributed. False, a linear combination of normally distributed random variables is normally distributed 14. The size of an 80 % confidence interval will not depend on the variance of the estimator used to generate the confidence interval.
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Problem Set 1 Solutions - Problem Set 1 Economics 103...

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