# HW 1AnswerKeys - Home assignment 01(answer keys Name 1 E X...

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Unformatted text preview: Home assignment 01 (answer keys) Name: 1. E ( X ) = 3 , V ar ( X ) = 1 ; E ( Y ) = 5 ; V ar ( Y ) = 4 ; Cov ( X;Y ) = 0 : 7 : Compute the followings. (a) Corr ( X;Y ) Corr [ X;Y ] = Cov [ X;Y ] p V ar [ X ] V ar [ Y ] = : 7 2 = 0 : 35 (b) Cov (3 X + 2 Y;Y ) Cov [3 X + 2 Y;Y ] = 3 Cov [ X;Y ] + 2 V ar [ Y ] = 3 & : 7 + 2 & 4 = 10 : 1 2. A study was recently done that emphasized the problem we all face with drinking and driving. Twenty accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: Case ID 1 2 3 4 5 6 7 8 9 10 Alcohol played a role? Y Y Y N N Y N Y N Y # of cars 1 1 2 1 2 2 1 1 3 2 Case ID 11 12 13 14 15 16 17 18 19 20 Alcohol played a role? N N Y N Y Y Y N Y Y # of cars 2 2 2 2 1 2 3 1 3 2 Let D = 1 if alcohol played a role in the event; 0 otherwise and X be the number of cars involved. (a) Compute the relative frequencies and &ll out the joint probability table below. X = 1 X = 2 X = 3 D = 1 4 = 20 6 = 20 2 = 20 D = 0 3 = 20 4 = 20 1 = 20 Which of the following does the table show? (1) f XD ( x;d ) (2) f X j D ( x j d ) (3) f D j X ( d;x )- (1) (b) Compute Corr ( D;X ) . (c) Compute E [ X ] . What does E [ X ] mean? E [ X ] = 1 & 7 20 + 2 & 10 20 + 3 & 3 20 = 9 5 = 1 : 8 1 E [ X ] means the average number of cars involved in an accident. (d) Compute E [ D ] . What does E [ D ] mean? E [ D ] = 1 & 12 20 + 0 & 8 20 = 3 5 = 0 : 6 E [ D ] means the average frequency (or probability) that alcohol is involved in an accident. (e) Provide f X j D ( x j d ) for d = 1 and d = 0 . f X j D ( x j d ) = f XD ( x;d ) f D ( d ) . Therefore X = 1 X = 2 X = 3 f X j D ( x j 1) 4 = 12 6 = 12 2 = 12 f X j D ( x j 0) 3 = 8 4 = 8 1 = 8 (f) Compute E [ X j D = 1] and E [ X j D = 0] . Interpret them....
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