For a certain group of​ states, it was observed that 60​% of the Democratic governors were succeeded by Democrats and 40​% by Republicans.​ Also, 20​% of the Republican governors were succeeded by Democrats and 80​% by Republicans.   ​(a) Set up the 2×2 stochastic matrix with columns and rows labeled D and R that displays these transitions. ​(b) Compute A2 and A3. ​(c) Suppose that all the current governors are Democrats. Assuming that the current trend holds for three​ elections, what percent of the governors will then be​ Democrats?       D R   ​(a) The stochastic matrix is D     nothing nothing       R nothing nothing ​(b) A2=         A3=         ​(c) nothing​% of the governors will be Democrats after three elections.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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For a certain group of​ states, it was observed that
60​%
of the Democratic governors were succeeded by Democrats and
40​%
by Republicans.​ Also,
20​%
of the Republican governors were succeeded by Democrats and
80​%
by Republicans.
 
​(a) Set up the
2×2
stochastic matrix with columns and rows labeled D and R that displays these transitions.
​(b) Compute
A2
and
A3.
​(c) Suppose that all the current governors are Democrats. Assuming that the current trend holds for three​ elections, what percent of the governors will then be​ Democrats?
 
 
 
D
R
 
​(a) The stochastic matrix is
D
 
 
nothing
nothing
 
 
 
R
nothing
nothing
​(b) A2=
   
   
A3=
   
   
​(c)
nothing​%
of the governors will be Democrats after three elections.
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