A golfer practices different parts of their game for hours. Specifically, the golfer practices: (1) putting, (2) their short game, and (3) their iron game. The amount of time spent on each part of their game is exponentially distributed. If the golfer is practicing their putting, they will always switch to their short game after an average of 30 minutes. When the golfer practices their short game, they do so for an average of 45 minutes, and then switches to putting with probability 0.6 or to their iron game with probability 0.4. When they practice their iron game, they do so for an average of 60 minutes. After practicing their iron game, the golfer will switch to putting or to their short game with
A golfer practices different parts of their game for hours. Specifically, the golfer practices: (1) putting, (2) their short game, and (3) their iron game. The amount of time spent on each part of their game is exponentially distributed. If the golfer is practicing their putting, they will always switch to their short game after an average of 30 minutes. When the golfer practices their short game, they do so for an average of 45 minutes, and then switches to putting with probability 0.6 or to their iron game with probability 0.4. When they practice their iron game, they do so for an average of 60 minutes. After practicing their iron game, the golfer will switch to putting or to their short game with
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A golfer practices different parts of their game for hours. Specifically, the golfer practices:
(1) putting, (2) their short game, and (3) their iron game. The amount of time spent on each part
of their game is exponentially distributed. If the golfer is practicing their putting, they will always
switch to their short game after an average of 30 minutes. When the golfer practices their short game,
they do so for an average of 45 minutes, and then switches to putting with probability 0.6 or to their
iron game with probability 0.4. When they practice their iron game, they do so for an average of 60
minutes. After practicing their iron game, the golfer will switch to putting or to their short game with
equal probability.
(a) Draw the CTMC rate diagram, clearly label your states and transition rates (qij ’s)
(b) Find the transition rates out of the states (vi’s) and transition probabilities (Pij ’s).
(c) Find the limiting probabilities (make sure to write out the balance equations).
(d) In the long run, what is the probability that the golfer is not putting?
(e) The golfer takes water breaks throughout practice. If they take a water break 10 percent
of the time when putting, 30 percent of the time when practicing their short game, and 50 percent
of the time when practicing their iron game, what proportion of the time does the golfer take a
water break?
(1) putting, (2) their short game, and (3) their iron game. The amount of time spent on each part
of their game is exponentially distributed. If the golfer is practicing their putting, they will always
switch to their short game after an average of 30 minutes. When the golfer practices their short game,
they do so for an average of 45 minutes, and then switches to putting with probability 0.6 or to their
iron game with probability 0.4. When they practice their iron game, they do so for an average of 60
minutes. After practicing their iron game, the golfer will switch to putting or to their short game with
equal probability.
(a) Draw the CTMC rate diagram, clearly label your states and transition rates (qij ’s)
(b) Find the transition rates out of the states (vi’s) and transition probabilities (Pij ’s).
(c) Find the limiting probabilities (make sure to write out the balance equations).
(d) In the long run, what is the probability that the golfer is not putting?
(e) The golfer takes water breaks throughout practice. If they take a water break 10 percent
of the time when putting, 30 percent of the time when practicing their short game, and 50 percent
of the time when practicing their iron game, what proportion of the time does the golfer take a
water break?
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(d) In the long run, what is the probability that the golfer is not putting?
(e) The golfer takes water breaks throughout practice. If they take a water break 10 percent
of the time when putting, 30 percent of the time when practicing their short game, and 50 percent
of the time when practicing their iron game, what proportion of the time does the golfer take a
water break?
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