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250 adults are practicing every day before taking part in a high-stakes children's game. The game requires them carefully to remove a shape- either a star or an umbrella- from a sugar wafer. 30% of those who choose stars on a given day will switch to umbrellas the next day, and 20% of those who choose umbrellas on a

250 adults are practicing every day before taking part in a high-stakes children's game. The game requires them carefully to remove a shape- either a star or an umbrella- from a sugar wafer. 30% of those who choose stars on a given day will switch to umbrellas the next day, and 20% of those who choose umbrellas on a

MATLAB: An Introduction with Applications
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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key Answer The corresponding Markov matrix is P = [0.7 0.2] 0.3 0.8 0.3] (If you choose to list umbrellas first and stars [0.8 0.3] second, then there is one other correct matrix: P = No other matrix is correct.) Using this 0.2 0.7 matrix, we find for part (a) that 125 are practicing with umbrellas tomorrow. For part (b), the unique steady- state vector (eigenvector of P with eigenvalue λ = 1 whose entries are positive and sum to 1) is [3/5]. S SO in the long run, 2/5 (or 40%) will be practicing with stars.
Transcribed Image Text:key Answer The corresponding Markov matrix is P = [0.7 0.2] 0.3 0.8 0.3] (If you choose to list umbrellas first and stars [0.8 0.3] second, then there is one other correct matrix: P = No other matrix is correct.) Using this 0.2 0.7 matrix, we find for part (a) that 125 are practicing with umbrellas tomorrow. For part (b), the unique steady- state vector (eigenvector of P with eigenvalue λ = 1 whose entries are positive and sum to 1) is [3/5]. S SO in the long run, 2/5 (or 40%) will be practicing with stars.
250 adults are practicing every day before taking part in a high-stakes children's game. The game requires them carefully to remove a shape- either a star or an umbrella- from a sugar wafer. 30% of those who choose stars on a given day will switch to umbrellas the next day, and 20% of those who choose umbrellas on a given day will switch to stars the next day. (a) If 150 contestants practice with stars today, how many will practice with umbrellas tomorrow? (b) If the actual game is held a long time from now, what proportion of contestants do we expect will be practicing with stars each day close to then?
Transcribed Image Text:250 adults are practicing every day before taking part in a high-stakes children's game. The game requires them carefully to remove a shape- either a star or an umbrella- from a sugar wafer. 30% of those who choose stars on a given day will switch to umbrellas the next day, and 20% of those who choose umbrellas on a given day will switch to stars the next day. (a) If 150 contestants practice with stars today, how many will practice with umbrellas tomorrow? (b) If the actual game is held a long time from now, what proportion of contestants do we expect will be practicing with stars each day close to then?
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