Download presentation

Presentation is loading. Please wait.

Published byElisabeth Purrington Modified over 2 years ago

1
MARKOV CHAIN A, B and C are three towns. Each year: 10% of the residents of A move to B 30% of the residents of A move to C 20% of the residents of B move to A 30% of the residents of B move to C 20% of the residents of C move to A 20% of the residents of C move to B Everybody else stays put. No one dies. No one is born.

2
A B C A, B, and C are three towns. 10 people live in A 15 people live in C 20 people live in B

3
A B C Each year 10% of the residents of A move to B.10 and 20% of the residents of A move to C.20

4
A B C.10.20 Each year 20% of the residents of B move to A.20 and 30% of the residents of B move to C.30

5
A B C.10.20.30 Each year 20% of the residents of C move to A.20 and 20% of the residents of C move to B.20

6
A B C.10.20.30.20

7
A B C.10.20.30.20

8
A B C.10.20.30.20

9
B A C.10.20.30.20 14 17 A B C 10 20 15 This year Next year Where will everyone be in 10 years?

11
A B C.10.20.30.20

12
A B C.10.20.30.20 A n+1 =.7A n

13
A C.10.20.30.20 A n+1 =.7A n +.2B n +.2C n B

14
A C.10.20.30.20 A n+1 =.7A n +.2B n +.2C n B n+1 =.1A n +.5B n +.2C n B

15
A C.10.20.30.20 A n+1 =.7A n +.2B n +.2C n B n+1 =.1A n +.5B n +.2C n C n+1 =.2A n +.3B n +.6C n B

16
A C.10.20.30.20 A n+1 =.7A n +.2B n +.2C n B n+1 =.1A n +.5B n +.2C n C n+1 =.2A n +.3B n +.6C n B

17
A n+1 =.7A n +.2B n +.2C n B n+1 =.1A n +.5B n +.2C n C n+1 =.2A n +.3B n +.6C n Note:.7+.1+.2 = 1. This accounts for 100% of those in town A in year n C n+1 =.2A n +.3B n +.6C n Note:.2+.5+.3 = 1. This accounts for 100% of those in town B in year nNote:.2+.2+.6 = 1. This accounts for 100% of those in town C in year n

20
Because the sum of the numbers in each column of M is 1, 1 is an eigenvalue for M, and An eigenvector belonging to 1 will describe stable proportions. The null space of 1I – M = the null space of -=

21
The null space of = Suppose there are this year 140 people in A, 80 people in B, and 130 people in C. How many will be in each town next year? ?

Similar presentations

OK

Mental Mind Gym coming …. 30 Second Challenge - Early Additive.

Mental Mind Gym coming …. 30 Second Challenge - Early Additive.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on alternative sources of energy Ppt on historical places in pune Ppt on understanding secularism in india Ppt on new zealand culture past Ppt on google driverless cars Ppt on media and entertainment industry Ppt on waxes for cars Module architecture view ppt on mac Ppt on hunter commission 1882 Ppt on classical economics states