c4solutions_0501 - COURSE 4 MAY 2001 MULTIPLE-CHOICE ANSWER...

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Course 4: May 2001 - 41 - STOP 1 D 26 A 2 B 27 E 3 C 28 E 4 E 29 D 5 C 30 C 6 C 31 A 7 D 32 A 8 E 33 A 9 D 34 D 10 A 35 E 11 D 36 D 12 E 37 B 13 B 38 B 14 C 39 E 15 A 40 C 16 C 17 E 18 A 19 B 20 E 21 C 22 E 23 B 24 B 25 C COURSE 4 MAY 2001 MULTIPLE-CHOICE ANSWER KEY
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C42001A Course 4 Exam Solutions May 2001 Item Number: 1 Key: D Solution Because the autocorrelation function is zero starting with lag 2, this must be an MA(1) model. Then, 22 1 1 1 111 2 1 . 4 , . 4 . 4 ,. 4 . 4 0. 1 q r q qqq q - -= = - - = - -+= + This quadratic equation has two roots, 0.5 and 2. Because the coefficient’s absolute value must be less than 1, only 0.5 is acceptable.
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C42001A Item Number: 2 Key: B Solution The posterior distribution is 2 / 3 2 4 /3 1 ( |2) 2 !3 e ee l ll l p - -- ∝∝ which is a gamma distribution with parameters 3 and 3/4. The variance is 3(3/4) 2 = 27/16.
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C42001A Item Number: 3 Key: C Solution ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 22222 2 2 44444 4 4 2 4 1 3 2 3 3 3 4 3 53 2 5 1 3 2 3 3 3 4 3 6.8 5 6.8 1.7 4 ms m m g s - +- +- +- +- = == ===
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C42001A Item Number: 4 Key: E Solution The calculations for each possibility are: Censored at 1 Censored at 2 Censored at 3 Censored at 4 Censored at 5 Time d Y $ S d Y $ S d Y $ S d Y $ S d Y $ S 1 0 5 1 1 5 .80 1 5 .80 1 5 .80 1 5 .80 2 1 4 .75 0 4 .80 1 4 .60 1 4 .60 1 4 .60 3 1 3 .50 1 3 .53 0 3 .60 1 3 .40 1 3 .40 4 1 2 .25 1 2 .27 1 2 .30 0 2 .40 1 2 .20 5 1 1 0 1 1 0 1 1 0 1 1 0 0 1 .20 This result may also be obtained by general reasoning. If the lapse occurs late, then the “death” times come earlier, leading to lower survival probabilities. If the lapse occurs early, then the “death” times come later, leading to higher survival probabilities.
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C42001A Item Number: 5 Key: C Solution This is testing 0 45 : 0, H bb == which is a joint test on several regression coefficients. The key formula is 5.21 (p.130 of Pindyck and Rubinfeld). We are given: R UR 2 094 = . Also, we know: N k = = 42 5 , (total number of coefficients to be estimated) and q = 2 Using 5.21, we obtain F = - - - = 0915 2 1 42 5 77 . . / . / . b g b g b g .
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