11. Mechanics. There are 7 M&M candies in a bag, three blue, two yellow, one red, and one orange. You reach into the bag and take one at random. If it is blue you put it back. If it is yellow or red you eat it with probability ½ and put it back with probability 3. If it is orange you { eat it and stop } with probability ½, and put it back with probability 1. You repeat the process until you stop. Define a Markov Chain precisely that you will use for each of the following problems. Define variables and write equations that if solved would give: (a) The expected number of iterations until you stop. (b) The probability that the bag contains one yellow and one red when you stop. (c) MODELING. The expected number of iterations until you stop, conditioned on the event that the bag contains one yellow and one red when you stop.
11. Mechanics. There are 7 M&M candies in a bag, three blue, two yellow, one red, and one orange. You reach into the bag and take one at random. If it is blue you put it back. If it is yellow or red you eat it with probability ½ and put it back with probability 3. If it is orange you { eat it and stop } with probability ½, and put it back with probability 1. You repeat the process until you stop. Define a Markov Chain precisely that you will use for each of the following problems. Define variables and write equations that if solved would give: (a) The expected number of iterations until you stop. (b) The probability that the bag contains one yellow and one red when you stop. (c) MODELING. The expected number of iterations until you stop, conditioned on the event that the bag contains one yellow and one red when you stop.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 16E: Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000...
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Transcribed Image Text:11. Mechanics. There are 7 M&M candies in a bag, three blue, two yellow, one red, and one
orange. You reach into the bag and take one at random. If it is blue you put it back. If it is
yellow or red you eat it with probability ½ and put it back with probability 3. If it is orange
you { eat it and stop } with probability ½, and put it back with probability 1. You repeat
the process until you stop.
Define a Markov Chain precisely that you will use for each of the following problems. Define
variables and write equations that if solved would give:
(a) The expected number of iterations until you stop.
(b) The probability that the bag contains one yellow and one red when you stop.
(c) MODELING. The expected number of iterations until you stop, conditioned on the
event that the bag contains one yellow and one red when you stop.
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