TEST BANK FOR INTRODUCTION TO ECONOMETRICS 3RD EDITION JAMES 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)  = E(Y )  (0  0.25)  (1 0.50)  (2  0.25)  1.00 . F d Using Key Concept 2.3: var(Y )  E(Y 2 ) [E(Y )]2 , and Fq, . so that (ui |Xi ) var(Y )  E(Y 2 ) [E(Y )]2  1.50  (1.00)2  0.50. 2.2. We know from Table 2.2 that Pr (Y  0)  022, Pr( X  1)  070. So Pr (Y  1)  078, Pr ( X  0)  030, (a) Y  E(Y )  0  Pr (Y  0)  1 Pr (Y  1)  0  022  1 078  078, X  E( X )  0  Pr ( X  0)  1 Pr ( X  1)  0  030  1 070  070 (b)  2  E[( X   )2 ] X X  (0  0.70)2  Pr ( X  0)  (1  0.70)2  Pr ( X  1)  (070)2  030  0302  070  021,  2  E[(Y   )2 ]  (0  0.78)2  Pr (Y  0)  (1  0.78)2  Pr (Y  1)  (078)2  022  0222  078  01716