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:

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 51E
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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
Employment
Last Year
This Year
Percentage
Industry
Industry
60
Small Business
10
Self-Employed
30
Small Business
Industry
10
Small Business
40
Self-Employed
50
Self-Employed
Industry
20
Small Business
20
Self-Employed
60
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).)
Transcribed Image Text:Employment Employment Last Year This Year Percentage Industry Industry 60 Small Business 10 Self-Employed 30 Small Business Industry 10 Small Business 40 Self-Employed 50 Self-Employed Industry 20 Small Business 20 Self-Employed 60 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.
P =
(2) Find the two-step transition matrix P(2):
P(2) =
(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.)
Transcribed Image Text:(1) Find the transition matrix for this Markov process. P = (2) Find the two-step transition matrix P(2): P(2) = (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.)
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