(3) What is the probability that an individual employed in industry at one time is employed in small business 2 years later? (4) If an individual is self-employed this year, what is her most likely...

Please solve and show solutions for questions 3-5. Pleas refer to both attachments if needed to solve the questions.

Extracted text: (3) What is the probability that an individual employed in industry at one time is employed in small business 2 years later? (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.) (5) If an individual would like to be self-employed 2 years from now, what current employment status would give here 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.)


Extracted text: Employment Employment Last Year This Year Percentage Industry Industry 80 Small Business 10 Self-Employed 10 Small Business Industry 10 Small Business 60 Self-Employed 30 Self-Employed Industry 30 Small Business 50 Self-Employed 20 Assume that state 1 is Industry, that state 2 is Small 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. 0.80 0.10 0.10 P = 0.10 0.60 0.30 0.30 0.50 0.20 (2) Find the two-step transition matrix P(2): 0.68 0.19 0.13 P(2) = 0.23 0.52 0.25 0.35 0.43 0.22