# 545454 0272727 0181818 converting the answer to

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6⇡2 + .3⇡3 ⇡1 + ⇡2 + ⇡3 = ⇡1 = ⇡2 =1 Subtracting ⇡1 from both sides of the ﬁrst equation and ⇡2 from both sides of the second, this translates into ⇡ A = (0, 0, 1) with 0 1 .2 .1 1 .4 1A A = @ .2 .3 .3 1 Note that here and in the previous example the ﬁrst two columns of A consist of the ﬁrst two columns of the transition probability with 1 subtracted from the diagonal entries, and the ﬁnal column is all 1’s. Computing the inverse and reading the last row gives (0.545454, 0.272727, 0.181818) Converting the answer to fractions using the ﬁrst entry in the MATH menu gives (6/11, 3/11, 2/11) To check this we note that 6/11 = ✓ 0 .8 3/11 2/11 @.2 .3 4.8 + .6 + .6 11 1 .1 .2A .4 .1 .6 .3 .6 + 1.8 + .6 11 .6 + .6 + .8 11 ◆ Example 1.20. Basketball (continuation of 1.10). To ﬁnd the stationary matrix in this case we can follow the same procedure. A consists of the ﬁrst three columns of the transition matrix with 1 subtracted from the diagonal, and a ﬁnal column of all 1’s. 1/4 0 2/3 0 1 /4 0 1...
View Full Document

## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

Ask a homework question - tutors are online