A recent study done by an economist for the Small Business Administration investigated failures of small business. Failures were either classified as due to poor financing, poor management, or a poor product. The failure rates differed for new businesses (under one year old) versus established businesses (over one year old.)
As the result of the economist's study, the following probabilities were determined. For new businesses the probability of failure due to financing was .15, due to management .20, and due to product .05. The corresponding probabilities for established businesses were .10, .06, and .03 respectively.
a.Determine a five-state Markov Chain transition matrix with states for new, established, and each of the three failure states. Write it in the form of I, O, R, and Q submatrices.
b.Determine the probability that a new business will survive during the next three years.
c.What proportion of new businesses eventually fail due to:(1) poor financing? (2) poor management? (3) poor product?

Question

A recent study done by an economist for the Small Business Administration investigated failures of small business. Failures were either classified as due to poor financing, poor management, or a poor product. The failure rates differed for new businesses (under one year old) versus established businesses (over one year old.)
As the result of the economist's study, the following probabilities were determined. For new businesses the probability of failure due to financing was .15, due to management .20, and due to product .05. The corresponding probabilities for established businesses were .10, .06, and .03 respectively.
a.​Determine a five-state Markov Chain transition matrix with states for new, established, and each of the three failure states. Write it in the form of I, O, R, and Q submatrices.
b.Determine the probability that a new business will survive during the next three years.
c.What proportion of new businesses eventually fail due to:(1) poor financing? (2) poor management? (3) poor product?

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The Answer of A recent study done by an economist for the Small Business Administration investigated failures of small business. Failures were either classified as due to poor financing, poor management, or a poor product. The failure rates differed for new businesses (under one year old) versus established businesses (over one year old.)
As the result of the economist's study, the following probabilities were determined. For new businesses the probability of failure due to financing was .15, due to management .20, and due to product .05. The corresponding probabilities for established businesses were .10, .06, and .03 respectively.
a.​Determine a five-state Markov Chain transition matrix with states for new, established, and each of the three failure states. Write it in the form of I, O, R, and Q submatrices.
b.Determine the probability that a new business will survive during the next three years.
c.What proportion of new businesses eventually fail due to:(1) poor financing? (2) poor management? (3) poor product?

A Recent Study Done by an Economist for the Small