In an experiment, you are trying to find out how many drones there are in an undiscovered planet. Here is the following plan: you are going to catch some drones and tag them, and then release them back into the wild. At some point, you are going to re-catch some number of drones. If most of the re-caught drones are tagged, you have reason to think that you caught most of the drones originally. If very few drones are caught in the second attempt, it would be reasonable to think that there were a lot more drones than what you caught initially. Suppose you initially catch 500 drones, tag them, and release them. At some point later, you re- catch a new 500 drones and find that 300 are tagged. Let's assume drones were equally likely to be caught at all times. a) What is the smallest number of drones that might be out there? b) What is the probability of the given scenario happening (the specific catch totals) as a function of N, where N is the number of drones out there? c) What number of N maximizes the likelihood of these results? d) Re-do parts a, b, and c in a more general setting, with N as the total number of drones, n1
In an experiment, you are trying to find out how many drones there are in an undiscovered planet. Here is the following plan: you are going to catch some drones and tag them, and then release them back into the wild. At some point, you are going to re-catch some number of drones. If most of the re-caught drones are tagged, you have reason to think that you caught most of the drones originally. If very few drones are caught in the second attempt, it would be reasonable to think that there were a lot more drones than what you caught initially. Suppose you initially catch 500 drones, tag them, and release them. At some point later, you re- catch a new 500 drones and find that 300 are tagged. Let's assume drones were equally likely to be caught at all times. a) What is the smallest number of drones that might be out there? b) What is the probability of the given scenario happening (the specific catch totals) as a function of N, where N is the number of drones out there? c) What number of N maximizes the likelihood of these results? d) Re-do parts a, b, and c in a more general setting, with N as the total number of drones, n1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Answer the following questions accordingly. I thank you in advance!
Transcribed Image Text:In an experiment, you are trying to find out how many drones there are in an undiscovered planet. Here is the following plan: you are going to catch some drones and tag them, and then release them back into the wild. At some point, you are going to re-catch some number of drones. If most of the re-caught drones are tagged, you have reason to think that you caught most of the drones originally. If very few drones are caught in the second attempt, it would be reasonable to think that there were a lot more drones than what you caught initially.
Suppose you initially catch 500 drones, tag them, and release them. At some point later, you re-catch a new 500 drones and find that 300 are tagged. Let’s assume drones were equally likely to be caught at all times.
a) What is the smallest number of drones that might be out there?
b) What is the probability of the given scenario happening (the specific catch totals) as a function of N, where N is the number of drones out there?
c) What number of N maximizes the likelihood of these results?
d) Re-do parts a, b, and c in a more general setting, with N as the total number of drones, n₁ as the number caught and tagged the first time, and n₂ caught and tagged the second time.
*** I need all parts to be done please (the first two parts aren’t that much work). I thank you in advance! ***
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