Explanation Given: The matrix is [ 1 .5 0 0 0 0 .5 0 0 .5 0 0 0 0 .5 1 ] . Approach: Consider the formula to compute the steady-state matrix for an absorbing stochastic matrix An absorbing stochastic matrix A has been partitioned into submatrices. A = [ I 0 | S R ] … (1) Then, the steady-state matrix of A is given by A = [ I 0 | S ( I - R ) - 1 0 ] … (2) Here, I is an identity matrix, 0 is the zero matrix and the order of the identity matrix appearing in the expression ( I − R ) − 1 is chosen to have the same order as R . Calculation: The given matrix is [ 1 .5 0 0 0 0 .5 0 0 .5 0 0 0 0 .5 1 ] . Rewrite the given matrix in the form of that the absorbing states appear first, partition the resulting matrix and identify the submatrices R and S . [ 1 0 0 0 0 1 0 0 | .5 0 0 .5 0 .5 .5 0 ] Comparing the matrix element from the equation (1). Here, the place of I is 1 , the place of zero matrix is 0 , the place of S is [ .5 0 0 .5 ] and the place of R is [ 0 .5 .5 0 ] . Now, calculate the matrix of S ( I − R ) − 1 . S ( I − R ) − 1 = ( [ .5 0 0 .5 ] ) ( [ 1 0 0 1 ] − [ 0 .5 .5 0 ] ) − 1 = ( [ .5 0 0 .5 ] ) ( [ 1 − .5 − .5 1 ] ) − 1 = ( [ .5 0 0

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Chapter 9.3, Problem 26E

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The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.

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Chapter 9.3, Problem 25E

Chapter 9.3, Problem 27E

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The probability that Diane can be leave the game a winner if she started with a capital of $ 1 and $ 2 .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

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To find:

The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.

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Chapter 9 Solutions

The probability that Diane can be leave the game a winner if she started with a capital of $ 1 and $ 2 .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

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To find: The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.

Want to see the full answer?

Chapter 9 Solutions

To find:

The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.