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 E Y μ . False, var(Y) = E[(Y- μ y ) 2 ] 4. Two random variables X and Y are independently distributed if ( ) [ ( | ) ] E Y E E Y 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 μ σ . Moving from the mean ( μ ) 1.64 standard deviations to the left and 1.64 standard deviations to the right, then the area under the
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