Question: 7. Assume reversibility. By passing the term along the product, we may see that i1 pi1,i2 pi2,i3 pin ,i1 = pi2,i1

7. Assume reversibility. By passing the π term along the product, we may see that

πi1 pi1,i2 pi2,i3 · · · pin ,i1 = pi2,i1 pi3,i2 · · · pi1,inπi1 . For the converse, sum over the intermediate j2, . . . , jn−1 to obtain p j1, jn (n − 1)p jn, j1 = pj1, jn pjn, j1(n − 1), and let n →∞.

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