12. The number of new individuals in a population of animals is sometimes approximated by calculating the expected number of survivors of the new born animals from the next genera- tion. The idea is that the number of new animals born follows some probability distribution, and the number of animals that survive depend on how many are present.¹ One example of a survivor function is the following: S₁(k) where b and c are real numbers with 0 < c < 1 based on the idea that more new born individuals increases competition and reduces the success rate to survive. Another example of a survivor function is S₂(k) = = b. ck, k {6 0 = 0≤k ≤ 2, otherwise. The idea is that once the number of newborns are above a certain level there are not enough resources for any to survive. (a) Determine E[S₁] if the number of newborns follows a Poisson distribution with mean A. (This is the derivation of the Ricker model which is used to model parasitic species.)
12. The number of new individuals in a population of animals is sometimes approximated by calculating the expected number of survivors of the new born animals from the next genera- tion. The idea is that the number of new animals born follows some probability distribution, and the number of animals that survive depend on how many are present.¹ One example of a survivor function is the following: S₁(k) where b and c are real numbers with 0 < c < 1 based on the idea that more new born individuals increases competition and reduces the success rate to survive. Another example of a survivor function is S₂(k) = = b. ck, k {6 0 = 0≤k ≤ 2, otherwise. The idea is that once the number of newborns are above a certain level there are not enough resources for any to survive. (a) Determine E[S₁] if the number of newborns follows a Poisson distribution with mean A. (This is the derivation of the Ricker model which is used to model parasitic species.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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![12. The number of new individuals in a population of animals is sometimes approximated by
calculating the expected number of survivors of the new born animals from the next genera-
tion. The idea is that the number of new animals born follows some probability distribution,
and the number of animals that survive depend on how many are present.¹ One example of
a survivor function is the following:
S₁(k)
b.ck.
where b and c are real numbers with 0 < c < 1 based on the idea that more new born
individuals increases competition and reduces the success rate to survive. Another example
of a survivor function is
S₂(k)
=
{
k
=
0 ≤k ≤ 2,
otherwise.
The idea is that once the number of newborns are above a certain level there are not enough
resources for any to survive.
(a)
Determine E[S₁] if the number of newborns follows a Poisson distribution with
mean X. (This is the derivation of the Ricker model which is used to model parasitic
species.)
(b)
Determine E[S2] if the number of newborns follows a Negative Binomial distri-
bution with probability of success is p and number of trials before stopping is r. (You
may have to look up the distribution function MF probability mass function) on
Wikipedia.) (This is similar to the method used to derive the Hassel model which use
used to model species who directly compete with each other.)
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73b64808-a9a4-4d5e-8109-1bcc6fca5ef9%2F65452ad6-6949-4878-b0c1-3273ece44215%2Fwlztw9v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12. The number of new individuals in a population of animals is sometimes approximated by
calculating the expected number of survivors of the new born animals from the next genera-
tion. The idea is that the number of new animals born follows some probability distribution,
and the number of animals that survive depend on how many are present.¹ One example of
a survivor function is the following:
S₁(k)
b.ck.
where b and c are real numbers with 0 < c < 1 based on the idea that more new born
individuals increases competition and reduces the success rate to survive. Another example
of a survivor function is
S₂(k)
=
{
k
=
0 ≤k ≤ 2,
otherwise.
The idea is that once the number of newborns are above a certain level there are not enough
resources for any to survive.
(a)
Determine E[S₁] if the number of newborns follows a Poisson distribution with
mean X. (This is the derivation of the Ricker model which is used to model parasitic
species.)
(b)
Determine E[S2] if the number of newborns follows a Negative Binomial distri-
bution with probability of success is p and number of trials before stopping is r. (You
may have to look up the distribution function MF probability mass function) on
Wikipedia.) (This is similar to the method used to derive the Hassel model which use
used to model species who directly compete with each other.)
-
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