Redo exercises 21 through 23 in section 8.2 of your textbook, about the three types of employment in a small town, using the following data: ### Employment Transition DataThe table below presents employment transitions from last year to this year, along with the percentage of individuals transitioning between different employment states. The states are categorized as Industry, Small Business, and Self-Employed.| Employment Last Year | Employment This Year | Percentage ||----------------------|----------------------|------------|| Industry | Industry | 60% || Industry | Small Business | 10% || Industry | Self-Employed | 30% || Small Business | Industry | 10% || Small Business | Small Business | 40% || Small Business | Self-Employed | 50% || Self-Employed | Industry | 20% || Self-Employed | Small Business | 20% || Self-Employed | Self-Employed | 60% |### Assumptions:- **State 1** is **Industry**- **State 2** is **Small Business**- **State 3** is **Self-Employed**#### Note:When answering related questions, express your answers as decimal fractions rounded to 4 decimal places if they extend beyond four decimal places. **Markov Process Transition Matrix Exercises****(1) Find the transition matrix for this Markov process.**The transition matrix $ P $ is structured as follows:\[P = \begin{bmatrix}\text{[cell]} & \text{[cell]} & \text{[cell]} \\\text{[cell]} & \text{[cell]} & \text{[cell]} \\\text{[cell]} & \text{[cell]} & \text{[cell]}\end{bmatrix}\]**(2) Find the two-step transition matrix $ P(2) $:**The two-step transition matrix $ P(2) $ is given by:\[P(2) =\begin{bmatrix}\text{[cell]} & \text{[cell]} & \text{[cell]} \\\text{[cell]} & \text{[cell]} & \text{[cell]} \\\text{[cell]} & \text{[cell]} & \text{[cell]}\end{bmatrix}\]**(3) What is the probability that an individual employed in industry at one time is employed in small business 2 years later?**\[\text{[cell]}\]**(4) If an individual is self-employed this year, what is her most likely employment status 2 years from now?**Provide the number of the state rather than its description in words. If there is more than one such state, choose the first one.\[\text{[cell]}\]**(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?**Provide the number of the state rather than its description in words. If there is more than one such state, choose the first one.\[\text{[cell]}\]

Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve. 1. let State 1 is Industry, State 2 is small business and State 3 is Self employed. From the given information, the transition matrix for this Markov process is obtained as- P=0.600.100.300.100.400.500.200.200.60 2. The two-step transition matrix is obtained as- P2=P×P=0.600.100.300.100.400.500.200.200.60×0.600.100.300.100.400.500.200.200.60=0.430.160.410.20.270.530.260.220.52 3. The required probability that an individual employed in industry at one time is employed in small business two years later is obtained as- PX2=2|X0=1=0.16 From two-step transition matrix

Answered: Redo exercises 21 through 23 in section…

Math

Statistics

Redo exercises 21 through 23 in section 8.2 of your textbook, about the three types of employment in a small town, using the following data:

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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