2008 hw4 key

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[Problem 1:
Viterbi path with z=1:
index start stop
 [1,]   14   75
 [2,]  106  141
 [3,]  185  195
 [4,]  222  226
 [5,]  303  316
 [6,]  347  375
 [7,]  420  442
 [8,]  454  479
 [9,]  572  610
[10,]  649  663
[11,]  684  694
[12,]  709  728
[13,]  749  812
[14,]  885  897
[15,]  902  922
[16,]  947 1000

Problem 2:
see attached

Problem 3:
see attached

lambda
0.9497487

mu0
-0.6108468 -0.6883153

mu1
0.5345843 0.4400449

sigma0 
0.5262309 0.4528901
0.4528901 1.0510932

sigma1
0.7194989 0.1265919
0.1265919 0.2571857

Problem 4:
see attached

lambda (with fixed parameters from question 3)
init	 	estimate
0.001	0.9552628
0.25		0.9553155
0.65		0.955164

lambda (with fixed parameters from question 1)
0.001	0.9594294
0.25		0.9594421
0.95		0.9594467

extra credit

lambda
0.9603218

mu0
-0.5021184 -0.5168662

mu1
0.4639936  0.5031449

sigma0
0.5622122 0.486025
0.4860250 1.061289

sigma1
0.6913180 0.1481361
0.1481361 0.3171098
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