### Employment Transition DataThis table presents the employment transition percentages from various sectors last year to this year:| Employment | Employment | ||--------------------|---------------|----------|| Last Year | This Year | Percentage || **Industry** | **Industry** | 60 || | **Small Business** | 20 || | **Self-Employed** | 20 || **Small Business** | **Industry** | 10 || | **Small Business** | 70 || | **Self-Employed** | 20 || **Self-Employed** | **Industry** | 80 || | **Small Business** | 10 || | **Self-Employed** | 10 |### Transition MatrixAssume:- **State 1:** Industry- **State 2:** Small Business- **State 3:** Self-Employed(Note: Express your answers as decimal fractions rounded to 4 decimal places.)#### Task:1. **Find the transition matrix** for this Markov process.\[ P = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix} \] **(2)** Find the two-step transition matrix $ P(2) $:\[ P(2) = \begin{bmatrix} \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \end{bmatrix}\]**(3)** What is the probability that an individual employed in industry at one time is employed in small business 2 years later?\[ \boxed{} \]**(4)** If an individual is self-employed this year, what is her most likely employment status 2 years from now? (Give the number of the state rather than its description in words.) (If there is more than one such state, which is the first one.)\[ \boxed{} \]**(5)** If an individual would like to be self-employed 2 years from now, what current employment status would give her the greatest likelihood of achieving her goal? (Give the number of the state rather than its description in words.) (If there is more than one such state, which is the first one.)\[ \boxed{} \]

Name: ### Employment Transition DataThis table presents the employment tran
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Description: ### Employment Transition DataThis table presents the employment transition percentages from various sectors last year to this year:| Employment | Employment | ||--------------------|---------------|----------|| Last Year

As per honor code, we will only provide answer for first three parts: 1) The transition matrix for this Markov process is given as: P=T11T12T13T21T22T23T31T32T33 T11=0.60, T12=0.20, T13=0.20T21=0.10, T22=0.70, T23=0.20T31=0.80, T32=0.10, T33=0.10P=0.600.200.200.100.700.200.800.100.10 2) P(2)=P·P=0.600.200.200.100.700.200.800.100.100.600.200.200.100.700.200.800.100.10=0.6×0.6+0.2×0.1+0.2×0.80.6×0.2+0.2×0.7+0.2×0.10.6×0.2+0.2×0.2+0.2×0.10.1×0.6+0.7×0.1+0.2×0.80.1×0.2+0.7×0.7+0.2×0.10.1×0.2+0.7×0.2+0.2×0.10.8×0.6+0.1×0.1+0.1×0.80.8×0.2+0.1×0.7+0.1×0.10.8×0.2+0.1×0.2+0.1×0.1=0.540.280.180.290.530.180.570.240.193) Required probability=P(2)12 =0.28 The probability that an individual employed in industry at one time is employed in small business 2 years later is 0.28.

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Statistics

Employment Employment Last Year This Year Percentage Industry Industry 60 Small Business 20 Self-Employed 20 Small Business Industry 10 Small Business 70 Self-Employed 20 Self-Employed Industry 80 Small Business 10 Self-Employed 10 Assume that state 1 is Industry, that state 2 is SmallI Business, and that state 3 is Self-Employed. (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) Find the transition matrix for this Markov process. P =

Employment Employment Last Year This Year Percentage Industry Industry 60 Small Business 20 Self-Employed 20 Small Business Industry 10 Small Business 70 Self-Employed 20 Self-Employed Industry 80 Small Business 10 Self-Employed 10 Assume that state 1 is Industry, that state 2 is SmallI Business, and that state 3 is Self-Employed. (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) Find the transition matrix for this Markov process. P =

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### Employment Transition Data

This table presents the employment transition percentages from various sectors last year to this year:

| Employment | Employment | |
|--------------------|---------------|----------|
| Last Year | This Year | Percentage |
| **Industry** | **Industry** | 60 |
| | **Small Business** | 20 |
| | **Self-Employed** | 20 |
| **Small Business** | **Industry** | 10 |
| | **Small Business** | 70 |
| | **Self-Employed** | 20 |
| **Self-Employed** | **Industry** | 80 |
| | **Small Business** | 10 |
| | **Self-Employed** | 10 |

### Transition Matrix

Assume:
- **State 1:** Industry
- **State 2:** Small Business
- **State 3:** Self-Employed

(Note: Express your answers as decimal fractions rounded to 4 decimal places.)

#### Task:

1. **Find the transition matrix** for this Markov process.

\[ P = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix} \]

**(2)** Find the two-step transition matrix $ P(2) $:

\[
P(2) = \begin{bmatrix}
\boxed{} & \boxed{} \\
\boxed{} & \boxed{} \\
\boxed{} & \boxed{}
\end{bmatrix}
\]

**(3)** What is the probability that an individual employed in industry at one time is employed in small business 2 years later?

\[ \boxed{} \]

**(4)** If an individual is self-employed this year, what is her most likely employment status 2 years from now? (Give the number of the state rather than its description in words.) (If there is more than one such state, which is the first one.)

\[ \boxed{} \]

**(5)** If an individual would like to be self-employed 2 years from now, what current employment status would give her the greatest likelihood of achieving her goal? (Give the number of the state rather than its description in words.) (If there is more than one such state, which is the first one.)

\[ \boxed{} \]

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