Hi Could you explain the question and answer to me in plain English? Please do what you can of the problem.?

Question

Hi Could you explain the question and answer to me in plain English?
Please do what you can of the problem.

You have a chain with N links numbered 1 through N. Every minute, you draw a random link from a bag, and connect it to any other consecutively-numbered link that you drew before. For example, if you drew 4,1,5,7,3, you would end up with three subchains: 1,(3,4,5),7. You keep on drawing until you have drawn all N links and connected them into a single chain of length N. Let M be the maximum number of subchains in this process.

What is the mean of the distribution of M if N=8
What is the standard deviation of the distribution of M if N=8
What is the mean of the distribution of M if N=16
What is the standard deviation of the distribution of M if N=16
What is the mean of the distribution of M if N=32
What is the standard deviation of the distribution of M if N=32
Please provide the script used to generate this result (max 10000 characters)
You can use
C/C++
Fortran
IDL
Java
Matlab
Perl
Python
R
Stata
SQL or
VBA

Answer 1

Alright, you have 5 chains in a bag. You pick a chain at random. Let's say it's chain number 2. After 1 draw, you have 1 subchain. The maximum number of subchains you've seen on this experiment run is 1.



Pick another. Say it's chain 4. Because 2 is not supposed to connect to 4, you don't connect them. After 2 draws, you have 2 subchains.The maximum number of subchains you've seen on this experiment run is 2.



Pick another. Say it's chain 1. Chain 1 connects to chain 2, so you connect them. After 3 draws, you have 2 subchains. The maximum number of subchains you've seen on this experiment run is 2.



Pick another. Say it's chain 3. Chain 3 connects to both 2 and 4, so you connect them. After 4 draws, you have 1 subchain. The maximum number of subchains you've seen on this experiment run is 2.



Pick your last chain (5). Connect it to chain 4. 5 draws, 1 subchain. Max subchains seen = 2.



You'll want to generalize your code to run the experiment with N chain links instead of just 5. They only seem to care about the maximum number of subchains seen, so you could just keep track of M through each experiment run. You'll want to run the experiment many times to get an average number for M for N chain links. Then you'll want to do this while varying N so that you can determine, experimentally, a relationship between N and your average M.



FYI, the way you are determining this falls under the category of Monte Carlo simulations.

Answer 2

Links numbered 1-N, does that mean it goes 1-10 and than A-N. Ughhh idk let me ask my ridiculously smart friend Mary.

Answer 3

ssss