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ps1_sol-1 - Introduction to Econometrics Professor Alexei...

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Introduction to Econometrics Professor Alexei Onastki Problem Set 1 – September 23 Problem 1) [ Stock and Watson 2.1 ] (a) Probability distribution function for Y Outcome (number of heads) Y = 0 Y = 1 Y = 2 probability 0.25 0.50 0.25 (b) Cumulative probability distribution function for Y Outcome (number of heads) Y < 0 0 Y < 1 1 Y < 2 Y 2 Probability 0 0.25 0.75 1.0 (c) = ( ) (0 0.25) (1 0.50) (2 0.25) 1.00 Y E Y μ = × + × + × = Using Key Concept 2.3: and 2 2 var( ) ( ) [ ( )] , Y E Y E Y = + × + × 2 2 (1 0.50) (2 0.25) = × = 2 2 ( ) (0 0.25) 1.50 E Y so that 2 2 2 var( ) ( ) [ ( )] 1.50 (1.00) 0.50. Y E Y E Y = = = Problem 2) [ Stock and Watson 2.6 ] The table shows that Pr( 0, 0) 0 045, X Y = = = . Pr( 0, 1) 0 709, X Y = = = . = = = . = = = . Pr( 1, 0) 0 005, X Y Pr( 1, 1) 0 241, X Y Pr( 0) 0 754, X = = . = = . 1) 0 246, Pr( X = = . Pr( 0) 0 Y 050, = = . Pr( 1) 0 950. Y (a) = = × = + × = = × . + × . = . . ( ) 0 Pr( 0) 1 Pr( 1) 0 0 050 1 0 950 0 950 Y E Y Y Y μ
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