Question

Use the age transition matrix L and the age distribution vector X, to find the age distribution vectors X, and X3. Then find a stable age distribution vector 0 3 12 1 0 0 600 600 600 0 % 0 X3 VIL DUO OD Find a stable age distribution vector

Answer 1

ری 12 1, - о О 1/6 о X 600 Соо Б06 We know that Untu 2 Хи 3 12 300 80 Х, 100 о 0 о І. о Соо fox600 + 3xboo+ 12xtoo) 2 1х200 + ox600 to x:00 ox600 + 4 +€004 oxcog до 00 боб с 100 Now X3 Lx2 - مد 12 о 9000 боо | | о о 0 1/6 Тоо

3 X 600 0x9000 + + 12 x 100 کیا 1x9000 + 0x600 + oxloo /x600 + 0x100 oxgooo t 3000 9000 X₂ - 100 Now the stable distribution Vector ago 0 12 I 0 0 1/6 a o . 3 12 1- λΙ 1 -N o 0 -1 Detoununaut -1 (1:0) -3(-1) +12 ( 16) = 0 -X 13 +3 À +2 = 0 13 - 3 1 -2 = 0 (1-2) (A +I) (+1) = 0 80 the roots are 1, -2, Ag = -1 12=-1,

Stable age distribution vector fo 1 = 2 we have ܟܫ 12 2 3 I 2 - O 30 -220 16-2 0 166 Rit R/2) -3/2 1 -6 - 2 4/6 -2 0 R2 R2 - IxRI 1 - 3/2 -1/2 6 0 116 - 2 R2 - R21 (1/2) -3/2 -6 12 - 2 17 Roz - 1 R2 R₃ - 3/2 -6 1 -12 0 0 R, -) Ri - (-²) R2 - 24 Xos a X2 -12 0 18 ]

- 24 X 3 = 0 X 2 - 12 X3 = 0 Xi = 24 X 3 X2 = 1 2 X3 yeuerul saluth 2 4 Xg X = 12X3 X3 X3 = 1 24 レ s 12 Stable Age Distribution vector