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Is anyone here really good at math

kc78

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Nov 25, 2002
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Specifically in the statistics arena. It has been a long, long time since I had to do anything with Expected Value and Variance and I've got a problem that requires that knowledge. I just need to get some direction in how to head with it.
 
I just need to get some direction in how to head with it.
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That is the focus of my applied math degree that I backed into. And I am probably no help whatsoever. Go over to the actuary boards (they exist) or hit up someone on campus.
 
Specifically in the statistics arena. It has been a long, long time since I had to do anything with Expected Value and Variance and I've got a problem that requires that knowledge. I just need to get some direction in how to head with it.

I've got a version of Minitab and have some stats experience (specific to stuff I normally work on).

What's the question?
 
Not good at math, here. Really had to try hard to succeed. I did get an "A" in statistics in college, but for me, if I don't use it I lose it.
 
Also there's a physics forum with a section where people help with a lot of different math topics.
 
I just need a bit of direction in what the math wants so I can write the program to solve this.

Smith College is a residential women's liberal arts college in Northampton, MA that is steeped in tradition. One such tradition is to give each student at graduation a diploma at random. At the end of the ceremony, a diploma circle is formed, and students pass the diplomas that they receive to the person next to them, and step out once they've received their diploma. What is the expected number of students who receive their diplomas in the initial disbursement?

The analytic solution (of the expect value) is easy to derive. Let $X_i$ is the event that $ith$ student receives their diploma then $E(X_i)=1/n$, for all i (the diplomas are uniformly distributed). n is the number of diplomas (students). Thus, if $Y$ is the sum of all the events $X_i$, then $E(Y)=1$. It is sometimes kind of surprising that the expected number of students receiving their diplomas in the initial disbursement does not depend on $n$. The variance can be more difficult to derive since $X_i$ are dependent.

Simulate the problem and find the expected value and the variance of the number of students who receive their diplomas in the initial giving.

My initial thought was to create a vector with 100 values in sequential order, another vector with 100 values randomized, and to then just loop through it to see how many match since it just wants the initial observation. But since it asks about expected value and variance I'm assuming it needs something more and I'm a bit lost.
 
I just need a bit of direction in what the math wants so I can write the program to solve this.

Smith College is a residential women's liberal arts college in Northampton, MA that is steeped in tradition. One such tradition is to give each student at graduation a diploma at random. At the end of the ceremony, a diploma circle is formed, and students pass the diplomas that they receive to the person next to them, and step out once they've received their diploma. What is the expected number of students who receive their diplomas in the initial disbursement?

The analytic solution (of the expect value) is easy to derive. Let $X_i$ is the event that $ith$ student receives their diploma then $E(X_i)=1/n$, for all i (the diplomas are uniformly distributed). n is the number of diplomas (students). Thus, if $Y$ is the sum of all the events $X_i$, then $E(Y)=1$. It is sometimes kind of surprising that the expected number of students receiving their diplomas in the initial disbursement does not depend on $n$. The variance can be more difficult to derive since $X_i$ are dependent.

Simulate the problem and find the expected value and the variance of the number of students who receive their diplomas in the initial giving.



In the initial disbursement, it is expected that 69 out 420 females will receive their diploma. If the expected number had been 70, then 350 women would be left without a degree after the first go-around.
 
I just need a bit of direction in what the math wants so I can write the program to solve this.



My initial thought was to create a vector with 100 values in sequential order, another vector with 100 values randomized, and to then just loop through it to see how many match since it just wants the initial observation. But since it asks about expected value and variance I'm assuming it needs something more and I'm a bit lost.
Is the answer potato?
 
sounds like a binomial distribution. mean = np
variance = np(1-p)

eta: google “example 7.17: the smith college diploma problem - SAS and R”
 
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I'm ok, my son was an Actuarial Science major, though, an works as an auditor for an insurance company. He deals with statistical analysis on a daily basis.
 
R is far, far better than SASS
This is for a class in R.

And I did see that problem, however that problem is asking a slightly different answer. It's asking how many rounds until everyone has the diploma. This one simply wants to know how many would have it after the first round. I can write a for loop to simulate that, but I'm not certain if it's asking for more.
 
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Is there not a package for this....my knowledge about R is in the geostatistics side
 
Is there not a package for this....my knowledge about R is in the geostatistics side
Not that I'm aware of.

I eventually did the following but I don't know if it's correct.

1. Created a vector of 1-100 to simulate 100 students
2. Created a vector which randomized the values from the student vector to represent the scrambled diplomas.
3. Created a loop to compare them 1 to 1 and sum a variable anytime they matched.

From there I determined the probability of success by dividing the number who matched by the number of students.

I determined the probability of failure by subtracting the above from 1.

I then determined the mean by multiplying the number of students by probability.
And the variance by multiplying numstudents * probability * probability of failure

Whether that's the correct math, I don't know but that's the best my google-fu can determine.
 
In the initial disbursement, it is expected that 69 out 420 females will receive their diploma. If the expected number had been 70, then 350 women would be left without a degree after the first go-around.

69 would have been my answer, also.
 
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If you know what the formula is you need to work with, this website is probably the greatest invention ever.

Mathway

Edit to add: hell sometimes you don’t even need to know the formula. It’ll ask you how you want to solve.
 
Not that I'm aware of.

I eventually did the following but I don't know if it's correct.

1. Created a vector of 1-100 to simulate 100 students
2. Created a vector which randomized the values from the student vector to represent the scrambled diplomas.
3. Created a loop to compare them 1 to 1 and sum a variable anytime they matched.

From there I determined the probability of success by dividing the number who matched by the number of students.

I determined the probability of failure by subtracting the above from 1.

I then determined the mean by multiplying the number of students by probability.
And the variance by multiplying numstudents * probability * probability of failure

Whether that's the correct math, I don't know but that's the best my google-fu can determine.

I'm sure there is a package for that and off hand what you did looks right
 
I just need a bit of direction in what the math wants so I can write the program to solve this.



My initial thought was to create a vector with 100 values in sequential order, another vector with 100 values randomized, and to then just loop through it to see how many match since it just wants the initial observation. But since it asks about expected value and variance I'm assuming it needs something more and I'm a bit lost.
That's more textbook math that I'm up for dealing with this week...😨
 
In the initial disbursement, it is expected that 69 out 420 females will receive their diploma. If the expected number had been 70, then 350 women would be left without a degree after the first go-around.
Was never good at story problems so could you expand on the 69?
 
This is what happens when you go to grad school in your mid-40s. Undergrad statistics was a long, long time ago. lol
Had I known this was "textbook" problems, I'd have passed.

I don't remember half the stuff in math/stats/physics classes I got A's in.
 
Not that I'm aware of.

I eventually did the following but I don't know if it's correct.

1. Created a vector of 1-100 to simulate 100 students
2. Created a vector which randomized the values from the student vector to represent the scrambled diplomas.
3. Created a loop to compare them 1 to 1 and sum a variable anytime they matched.

From there I determined the probability of success by dividing the number who matched by the number of students.

I determined the probability of failure by subtracting the above from 1.

I then determined the mean by multiplying the number of students by probability.
And the variance by multiplying numstudents * probability * probability of failure

Whether that's the correct math, I don't know but that's the best my google-fu can determine.

I believe this is an n! (factorial) problem.

You have 1 orientation all the students line up in, and n! (or (n-1)! or whatever) permutations the diplomas can be given out.

So, you simulate out of those permutations, the combined likelihoods of 1, 2, 3, ..... n students all getting their diplomas on the first handout.

There will be a different answer if you're computing the probability that 1 will get their diploma, vs what the question here is, the likely number that will. But I think you can simulate this with those combined/summed factorial calculations.
 
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