Econ 281 Fall 2010 Problem Set 1 - Solutions

Econ 281 Fall 2010 Problem Set 1 - Solutions - Econ 281...

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Econ 281 Fall Quarter 2010 Problem Set 1 - Solutions Solve the following Problems. Show your work. 1. Problems 2.2, 2.3, 2.7, 2.22 from book
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2. Use the following table to calculate a) – d). Y 1 2 X 2 0.15 0.22 3 0.25 0.38 a) Find E(X)=2.63 and E(Y)=1.6 b) Find P(X=2|Y=1)=.375 c) Find E(X|Y=2)= 2.6333 and E(X|Y=1)=2.625 d) Use the Law of Iterated Expectations to show the E(Y)=E X [E(Y|X)] E(Y)=1.594*.37 + 1.603*.63=1.6 e) Use the other version of the LIE to show that E(X*Y)=E X [X*E(Y|X] E(X*Y)=2*1*.15 + 2*2*.22 + 3*1*.25 +3*2*.38=4.21 E X [X*E(Y|X]2*E(Y|X=2)*P(X=2) + 3*E(Y|X=3)*P(X=3) =2*1.59*.37 +3*1.6*.63=4.21 3. In September Seattle’s daily high temperature has a mean of 60 degrees Fahrenheit and a standard deviation of 6 degrees Fahrenheit. Calculate the mean, variance, and standard deviation in degree Celsius. (Hint: 32 F = 0 C and 100C = 212F) Transformation: C = -160/9 +5/9*F E(C) = -160/9 + 5/9*60 = 140/9 = 15.55 V(C) = (5/9)2*36 = 100/9 = 11.11 SD(C) = Squareroot(100/9) = 10/3 = 3.33
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Econ 281 Fall 2010 Problem Set 1 - Solutions - Econ 281...

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