SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...

65
The expected number of spins is
which is the sum of the first row of
µ 00 + µ 01 + ···+ µ 09 ≈ 15.8
M = (I − P TT ) −1
⎛
5.642555330 1.237076756 1.468321920 1.508490981 1.699310675
4.430331574 2.051427403 1.388800859 1.464830124 1.619923520
4.189308265 0.9910305820 2.185061681 1.373952904 1.557546460
3.624339776 1.132212235 1.088206223 2.150572935 1.430445774
=
3.326241706 0.7736368034 1.211218915 1.044607959 2.189326947
2.944765281 0.7518819338 0.8321534392 1.159204127 1.064213430
2.502145104 0.5682528341 0.7588874323 0.7378123674 1.120907044
2.094007860 0.4917825124 0.5692601344 0.6742348636 0.6995152842
⎜
⎝ 1.721601833 0.3844024235 0.4797861159 0.4846075656 0.6262492773
1.404367293 0.3172345401 0.3724060269 0.4081372440 0.4426201777
⎞
1.105741430 1.019364871 0.9134948380 0.6768445448 0.5307779547
1.191625516 1.002037338 0.9081983520 0.6745406751 0.5394859830
1.126134901 1.081735894 0.8876763410 0.6647276567 0.5371821134
1.104626156 1.008894626 0.9654729638 0.6442056457 0.5318856274
1.000579145 0.9847916242 0.8926316951 0.7239042017 0.5145580951
1.792814119 0.8807446128 0.8711229501 0.6584135873 0.6004421813
0.6677006009 1.639625786 0.7440222642 0.5960365279 0.5210550255
0.7822967692 0.5336608097 1.520642295 0.5051593083 0.4773941689
⎟
0.4032312936 0.6566735018 0.4237868366 1.301420130 0.3978731088 ⎠
0.3814764240 0.2980980700 0.5649684897 0.2410233088 1.212223756
The distribution of the number of spins is f 0,10, (n) n =1, 2,...with A = {0, 1,...,9} and
B = {10} which is the (1, 1) element of F (n)
AB = P (n−1)
AA P AB .