In a survey it was found that 72 of the population of a cert

In a survey it was found that 72% of the population of a certain urban area lived in single-family dwellings and 28% in multiple housing. Five years later, of those who had been living in single-family dwellings, 89% still did so, but 11% had moved to multiple family dwellings. Of those in multiple housing 91% were still living in that type of housing, while 9% had moved to single-family housing. Answer the following questions assuming these trends continue. Fill in the appropriate transistion matrix for this information. Find the probability vector for the initial distribution of housing. The probability vector is What percent of the population can be expected in each category after 5years?

Solution

a) Transition Matrix :

| 0.72*0.89    0.72*0.11 |

| 0.28*0.09    0.28*0.91 |

=

| 0.64 0.079|

| 0.0252 0.254|

b) Probability Matrix of initial distribution :

=

[ 0.72 0.28 ]

c)

After 5 years , the % of population living in single family dwelling = ( 0.64 + 0.0252) = 0.66

After 5 years , the % of population living in miltiple family dwelling = ( 0.079 + 0.254 ) = 0.34