One way to measure the diversity of a population of organisms is to calculate its Gini-Simpson diversity index, H. In its simplest incarnation, consider a population of yeast cells; each yeast cell is one of two types (call them "red" and "green"). The diversity index of the population is the probability that if two cells are picked at random, they are different colors (i.e., one is red and the other is green). If p is the proportion of cells of red-type, the diversity index H can be calculated from p using the formula H(p) = 2p(1 – p), pE[0,1]. Conversely, one could ask what is the probability that the two individuals are genetically identical. Call this probability I(p). It is given by I(p) = 2p² - 2p + 1. Complete parts (a) through (c) below. (a) The function I(p) is known as the Simpson index. Explain why the domain of I is pe[0,1]. Choose the correct answer below. O A. The domain of H(p) is pe[0,1] and all related functions must have the same domain. O B. Substituting a negative value or a value greater than 1 for p in I(p) results in an undefined expression. OC. Since p is a proportion, it cannot be negative or greater than 1. O D. The coefficient of the squared term is a positive value greater than 1, so only positive values between 0 and 1 can be substituted for p in that term.
One way to measure the diversity of a population of organisms is to calculate its Gini-Simpson diversity index, H. In its simplest incarnation, consider a population of yeast cells; each yeast cell is one of two types (call them "red" and "green"). The diversity index of the population is the probability that if two cells are picked at random, they are different colors (i.e., one is red and the other is green). If p is the proportion of cells of red-type, the diversity index H can be calculated from p using the formula H(p) = 2p(1 – p), pE[0,1]. Conversely, one could ask what is the probability that the two individuals are genetically identical. Call this probability I(p). It is given by I(p) = 2p² - 2p + 1. Complete parts (a) through (c) below. (a) The function I(p) is known as the Simpson index. Explain why the domain of I is pe[0,1]. Choose the correct answer below. O A. The domain of H(p) is pe[0,1] and all related functions must have the same domain. O B. Substituting a negative value or a value greater than 1 for p in I(p) results in an undefined expression. OC. Since p is a proportion, it cannot be negative or greater than 1. O D. The coefficient of the squared term is a positive value greater than 1, so only positive values between 0 and 1 can be substituted for p in that term.
MATLAB: An Introduction with Applications
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![One way to measure the diversity of a population of organisms is to calculate its Gini-Simpson diversity index, H. In its simplest incarnation, consider a population of yeast cells; each yeast cell is one of two types (call them "red" and "green"). The diversity
index of the population is the probability that if two cells are picked at random, they are different colors (i.e., one is red and the other is green). If p is the proportion of cells of red-type, the diversity index H can be calculated from p using the formula
H(p) = 2p(1 – p), pE[0,1]. Conversely, one could ask what is the probability that the two individuals are genetically identical. Call this probability I(p). It is given by I(p) = 2p² - 2p + 1. Complete parts (a) through (c) below.
(a) The function I(p) is known as the Simpson index. Explain why the domain of I is pe[0,1]. Choose the correct answer below.
O A. The domain of H(p) is pe[0,1] and all related functions must have the same domain.
O B. Substituting a negative value or a value greater than 1 for p in I(p) results in an undefined expression.
OC. Since p is a proportion, it cannot be negative or greater than 1.
O D. The coefficient of the squared term is a positive value greater than 1, so only positive values between 0 and 1 can be substituted for p in that term.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2721ccf2-fbe1-4868-87fa-588e33d78a8e%2F73a8f9b1-488a-41bd-9648-c9a69ebd8e69%2Fxr16nv.png&w=3840&q=75)
Transcribed Image Text:One way to measure the diversity of a population of organisms is to calculate its Gini-Simpson diversity index, H. In its simplest incarnation, consider a population of yeast cells; each yeast cell is one of two types (call them "red" and "green"). The diversity
index of the population is the probability that if two cells are picked at random, they are different colors (i.e., one is red and the other is green). If p is the proportion of cells of red-type, the diversity index H can be calculated from p using the formula
H(p) = 2p(1 – p), pE[0,1]. Conversely, one could ask what is the probability that the two individuals are genetically identical. Call this probability I(p). It is given by I(p) = 2p² - 2p + 1. Complete parts (a) through (c) below.
(a) The function I(p) is known as the Simpson index. Explain why the domain of I is pe[0,1]. Choose the correct answer below.
O A. The domain of H(p) is pe[0,1] and all related functions must have the same domain.
O B. Substituting a negative value or a value greater than 1 for p in I(p) results in an undefined expression.
OC. Since p is a proportion, it cannot be negative or greater than 1.
O D. The coefficient of the squared term is a positive value greater than 1, so only positive values between 0 and 1 can be substituted for p in that term.
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