Genetics. A given plant species has red, pink, or white flowers according to the genotypes RR, RW. and WW, respectively. If each of these genotypes is crossed with a pink flowering plant (genotype RW), then the transition matrix is Next generation Re d P i n k W h i t e This generation Re d P i n k W h i t e .5 .5 0 .25 .5 .25 0 .5 .5 Assuming that the plants of each generation are crossed only with pink plants to produce the next generation, show that regardless of the makeup of the first generation, the genotype composition will eventually stabilize at 25 % red, 50 % pink, and 25 % white. (Find the stationary matrix.)
Genetics. A given plant species has red, pink, or white flowers according to the genotypes RR, RW. and WW, respectively. If each of these genotypes is crossed with a pink flowering plant (genotype RW), then the transition matrix is Next generation Re d P i n k W h i t e This generation Re d P i n k W h i t e .5 .5 0 .25 .5 .25 0 .5 .5 Assuming that the plants of each generation are crossed only with pink plants to produce the next generation, show that regardless of the makeup of the first generation, the genotype composition will eventually stabilize at 25 % red, 50 % pink, and 25 % white. (Find the stationary matrix.)
Solution Summary: The author proves that regardless of the makeup of first generation, the genotype composition will eventually stabilize at 25% red,
Genetics. A given plant species has red, pink, or white flowers according to the genotypes RR, RW. and WW, respectively. If each of these genotypes is crossed with a pink flowering plant (genotype RW), then the transition matrix is
Next generation
Re
d
P
i
n
k
W
h
i
t
e
This
generation
Re
d
P
i
n
k
W
h
i
t
e
.5
.5
0
.25
.5
.25
0
.5
.5
Assuming that the plants of each generation are crossed only with pink plants to produce the next generation, show that regardless of the makeup of the first generation, the genotype composition will eventually stabilize at
25
%
red,
50
%
pink, and
25
%
white. (Find the stationary matrix.)
If Joe is in C now, find the probability that he will be in A two weeks later.
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day.
a. Give the transition matrix.
b. if the air quality is good today, what is the probability it will be good two days from now?
c. if the air quality is bad today, what is the probability it will be bad three days from now?
d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?
Oc.
O D. The given matrix A not a transition matrix, so there is no diagram.
B
Chapter 9 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY