(b) 60 q is the transition matrix from age 60 to 61; 61 q is the transition matrix
from age 61 to 62.
(iii) the two models produce equal probabilities of decrement.
calculate 61 q .
(a)
1.00 0.12 0.09
0 1.00 0
0 0 1.00
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
(b)
0.80 0.12 0.09
0.56 0.16 0.09
0 0 1.00
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
(c)
0.76 0.16 0.09
0 1.00 0
0 0 1.00
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
(d)
0.70 0.20 0.10
0 1.00 0
0 0 1.00
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
(e)
0.60 0.28 0.12
0 1.00 0
0 0 1.00
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝ ⎠
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