Linear Algebra and Its Applications (5th Edition)
5th Edition
ISBN: 9780321982384
Author: David C. Lay, Steven R. Lay, Judi J. McDonald
Publisher: PEARSON
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Chapter 10.2, Problem 27E
(a)
To determine
To show: The probability of an offspring being dominant is
(b)
To determine
To show: The probability of an offspring being recessive is
(c)
To determine
To show: The probability of an offspring being dominant is
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Some traits of plants and animals depend on inheritance of a single gene. This is called Mendelian inheritance, after Gregor Mendel (1822-1884). Each of us has an ABO blood type, which describes whether two characteristics called A and B are present. Every human being has two blood type alleles (gene forms), one inherited from our mother and one from our father. Each of these alleles can be A, B, or O. Which two we inherit determines our blood type. Here is a table that shows what our blood type is for each combination of two alleles.
Alleles inherited
Blood type
A and A
A
A and B
AB
A and O
A
B and B
B
B and O
B
O and O
O
We inherit each of a parent's two alleles with probability 0.5. We inherit independently from our mother and father.
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person with only one sickle cell gene will have a mild, nonfatal anemia called sickle
cell trait. If we use s to represent
a sickle cell gene, and S a healthy gene, the
table shows the four possibilities for the
children of one healthy, SS parent, and one
parent with sicke cell trait, Ss. Find the
probability that these parents give birth to a
child who has sickle cell anemia.
S
Healthy
First Parent S
Second Parent
(with Sickle
Cell Trait)
S
SS
SS
The probability that the parents give birth to a child who has sickle cell anemia =
(Type an integer or a simplified fraction.)
S
Ss
Ss
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Chapter 10 Solutions
Linear Algebra and Its Applications (5th Edition)
Ch. 10.1 - Fill in the missing entries in the stochastic...Ch. 10.1 - Prob. 2PPCh. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - In Exercises 5 and 6, the transition matrix P for...Ch. 10.1 - Prob. 6ECh. 10.1 - In Exercises 7 and 8, the transition matrix P for...Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...
Ch. 10.1 - Consider a pair of Ehrenfest urns labeled A and B....Ch. 10.1 - Consider a pair of Ehrenfest urns labeled A and B....Ch. 10.1 - Consider an unbiased random walk on the set...Ch. 10.1 - Consider a biased random walk on the set {1,2,3,4}...Ch. 10.1 - In Exercises 13 and 14, find the transition matrix...Ch. 10.1 - In Exercises 13 and 14, find the transition matrix...Ch. 10.1 - In Exercises 15 and 16, find the transition matrix...Ch. 10.1 - In Exercises 15 and 16, find the transition matrix...Ch. 10.1 - The mouse is placed in room 2 of the maze shown...Ch. 10.1 - The mouse is placed in room 3 of the maze shown...Ch. 10.1 - Prob. 19ECh. 10.1 - In Exercises 19 and 20, suppose a mouse wanders...Ch. 10.1 - Prob. 21ECh. 10.1 - In Exercises 21 and 22, mark each statement True...Ch. 10.1 - The weather in Charlotte, North Carolina, can be...Ch. 10.1 - Suppose that whether it rains in Charlotte...Ch. 10.1 - Prob. 25ECh. 10.1 - Consider a set of five webpages hyperlinked by the...Ch. 10.1 - Consider a model for signal transmission in which...Ch. 10.1 - Consider a model for signal transmission in which...Ch. 10.1 - Prob. 29ECh. 10.1 - Another model for diffusion is called the...Ch. 10.1 - To win a game in tennis, one player must score...Ch. 10.1 - Volleyball uses two different scoring systems in...Ch. 10.1 - Prob. 33ECh. 10.2 - Consider the Markov chain on {1, 2, 3} with...Ch. 10.2 - In Exercises 1 and 2, consider a Markov chain on...Ch. 10.2 - Prob. 2ECh. 10.2 - In Exercises 3 and 4, consider a Markov chain on...Ch. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - In Exercises 5 and 6, find the matrix to which Pn...Ch. 10.2 - In Exercises 7 and 8, determine whether the given...Ch. 10.2 - Prob. 8ECh. 10.2 - Consider a pair of Ehrenfest urns with a total of...Ch. 10.2 - Consider a pair of Ehrenfest urns with a total of...Ch. 10.2 - Consider an unbiased random walk with reflecting...Ch. 10.2 - Consider a biased random walk with reflecting...Ch. 10.2 - Prob. 13ECh. 10.2 - In Exercises 13 and 14, consider a simple random...Ch. 10.2 - In Exercises 15 and 16, consider a simple random...Ch. 10.2 - In Exercises 15 and 16, consider a simple random...Ch. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Consider the mouse in the following maze, which...Ch. 10.2 - In Exercises 21 and 22, mark each statement True...Ch. 10.2 - In Exercises 21 and 22, mark each statement True...Ch. 10.2 - Prob. 23ECh. 10.2 - Suppose that the weather in Charlotte is modeled...Ch. 10.2 - In Exercises 25 and 26, consider a set of webpages...Ch. 10.2 - In Exercises 25 and 26, consider a set of webpages...Ch. 10.2 - Prob. 27ECh. 10.2 - Consider beginning with an individual of known...Ch. 10.2 - Prob. 29ECh. 10.2 - Consider the Bernoulli-Laplace diffusion model...Ch. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Let 0 p, q 1, and define P = [p1q1pq] a. Show...Ch. 10.2 - Let 0 p, q 1, and define P = [pq1pqq1pqp1pqpq]...Ch. 10.2 - Let A be an m m stochastic matrix, let x be in m...Ch. 10.2 - Prob. 37ECh. 10.2 - Consider a simple random walk on a finite...Ch. 10.2 - Prob. 39ECh. 10.3 - Consider the Markov chain on {1, 2, 3, 4} with...Ch. 10.3 - Prob. 1ECh. 10.3 - In Exercises 16, consider a Markov chain with...Ch. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Consider the mouse in the following maze from...Ch. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Consider an unbiased random walk with absorbing...Ch. 10.3 - In Exercises 13 and 14, consider a simple random...Ch. 10.3 - Prob. 14ECh. 10.3 - In Exercises 15 and 16, consider a simple random...Ch. 10.3 - In Exercises 15 and 16, consider a simple random...Ch. 10.3 - Consider the mouse in the following maze from...Ch. 10.3 - Consider the mouse in the following maze from...Ch. 10.3 - Prob. 19ECh. 10.3 - In Exercises 19 and 20, consider the mouse in the...Ch. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Suppose that the weather in Charlotte is modeled...Ch. 10.3 - Prob. 24ECh. 10.3 - The following set of webpages hyperlinked by the...Ch. 10.3 - The following set of webpages hyperlinked by the...Ch. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - In Exercises 33 and 34, consider the Markov chain...Ch. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.4 - Consider the Markov chain on {1, 2, 3, 4} with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 1-6, consider a Markov chain with...Ch. 10.4 - In Exercises 7-10, consider a simple random walk...Ch. 10.4 - In Exercises 7-10, consider a simple random walk...Ch. 10.4 - In Exercises 7-10, consider a simple random walk...Ch. 10.4 - In Exercises 7-10: consider a simple random walk...Ch. 10.4 - Reorder the states in the Markov chain in Exercise...Ch. 10.4 - Reorder the states in the Markov chain in Exercise...Ch. 10.4 - Reorder the states in the Markov chain in Exercise...Ch. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Find the transition matrix for the Markov chain in...Ch. 10.4 - Find the transition matrix for the Markov chain in...Ch. 10.4 - Consider the mouse in the following maze from...Ch. 10.4 - Consider the mouse in the following maze from...Ch. 10.4 - In Exercises 21-22, mark each statement True or...Ch. 10.4 - In Exercises 21-22, mark each statement True or...Ch. 10.4 - Confirm Theorem 5 for the Markov chain in Exercise...Ch. 10.4 - Prob. 24ECh. 10.4 - Consider the Markov chain on {1, 2, 3} with...Ch. 10.4 - Follow the plan of Exercise 25 to confirm Theorem...Ch. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.5 - Prob. 1PPCh. 10.5 - Consider a Markov chain on {1, 2, 3, 4} with...Ch. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - In Exercises 13, find the fundamental matrix of...Ch. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Consider a simple random walk on the following...Ch. 10.5 - Consider a simple random walk on the following...Ch. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Consider the mouse in the following maze from...Ch. 10.5 - In Exercises 21 and 22, mark each statement True...Ch. 10.5 - Prob. 22ECh. 10.5 - Suppose that the weather in Charlotte is modeled...Ch. 10.5 - Suppose that the weather in Charlotte is modeled...Ch. 10.5 - Consider a set of webpages hyperlinked by the...Ch. 10.5 - Consider a set of webpages hyperlinked by the...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 27-30 concern the Markov chain model for...Ch. 10.5 - Exercises 31-36 concern the two Markov chain...Ch. 10.5 - Exercises 31-36 concern the two Markov chain...Ch. 10.5 - Exercises 31-36 concern the two Markov chain...Ch. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Consider a Markov chain on {1, 2, 3, 4, 5, 6} with...Ch. 10.5 - Consider a Markov chain on {1,2,3,4,5,6} with...Ch. 10.5 - Prob. 39ECh. 10.6 - Let A be the matrix just before Example 1. Explain...Ch. 10.6 - Prob. 2PPCh. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Major League batting statistics for the 2006...Ch. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - In the previous exercise, let p be the probability...
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