Question

Use the age transition matrix L and age distribution vector Xy to find the age distribution vectors X2 and X3. 0 2 0 0 0 16 16 L = 2 X1 = 16 0 x2 = X3 = IND 10 Then find a stable age distribution vector. X=t

Answer 1

0 28 O 2 SejmThe geven age fransition musia L= age and distribution vector is IC Now, we obtain age distribution-vector X2 and dz as follows. It is known that Ant = Lan X = LX, ro 2 1 2 32 8 O 0 140 Sinularly, Rz = LR2 2 7132 o 4 64 *3 = We need torch now, we find the stable are distribution vector: To find a stable age distribution vector tind an eigenvalue and eigen vector. IL DI so 7 2 O NL -7 o og - d+8 = 0 n a= 0, 1,-1 Choose the eigen value = 1, then the corresponding eigen vector is

2 2 0 a b 13 2 - -2 C to 2 0 -) ONI OOT 10.) a-2b = 0 ; b-40 = 0 a) a= 26 > b=40 a= se les e-t (ER) Then, 1819 - i's distribution vector Thus, a stable age x = t - Ans). Note: you Cem wie vector, = 0,- 1 to find the stable age distribution