Question

Use the age transition matrix L and the age distribution vector x; to find the age distribution vectors X2 and X3. Then find a stable age distribution vector. 0 3 10 1 0 0 500 500 500 0 0 Find a stable age distribution vector

Answer 1

Ay. LX, X2 and LX 22 X3. wahuse L is the age Transition matrin LX,= x2 0 3 10 Las Soo Souxis 6500 soo 2 soo 500 22 yo Soo 100 100 Laga X3 0 310 6500 0 O soo 6 500X1Q + 1500 t loxloo 65oo 1500 5 0 Vs 100 ། ། H3 1500t 1000 6500 100 13? 2500 6500 loo b. To find the stable age distribution recta we had to find and worsenedig eigen rector is the stable age dishu butin rector

Lax where xis stable distribution dictulution ye La-xIx TO I )x=0 det (2-1) =0 .. PIVE -> +31+2 = -A+1)(4-4-2) O >-(4+1) (x+1) (-2) 1.-4 1,2 05 - - - carreguending eignata t -5 whes, and by eigenvator 20 lo - 1232 1). as age is generally prostire io to2 aes podig eigurata distitution vector age which is ů stable 20 10