A  car agency has offices in  Phoenix,  Denver, and  Chicago.  The agency allows one-  or two-way rentals so that cars rented in one location may end up in another.  Statistics show that at the end of each week  70%  of all rentals are two-way.  As  for  the  one-way  rentals:  from  Phoenix,  40%  go to  Denver,  and  the  rest to  Chicago;  from  Denver,  60%  go  to  Chicago and  the  rest  to  Phoenix;  from Chicago,  40%  go  to  Denver  and  the  rest to  Phoenix;    If  the  agency  starts  the  week  with  100  cars  in  each  location,  what  will the  distribution  be  like  in  two  weeks  (two-step  transition  probability  matrix)?

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A  car agency has offices in  Phoenix,  Denver, and  Chicago.  The agency allows one-  or two-way rentals so that cars rented in one location may end up in another.  Statistics show that at the end of each week  70%  of all rentals are two-way.  As  for  the  one-way  rentals:  from  Phoenix,  40%  go to  Denver,  and  the  rest to  Chicago;  from  Denver,  60%  go  to  Chicago and  the  rest  to  Phoenix;  from Chicago,  40%  go  to  Denver  and  the  rest to  Phoenix;  

 If  the  agency  starts  the  week  with  100  cars  in  each  location,  what  will the  distribution  be  like  in  two  weeks  (two-step  transition  probability  matrix)? 

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