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.
Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
I just need to get some direction in how to head with it.
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 can recite most of the statistics off the 1986 and 1987 Topps Baseball Cards. I think I'm your man.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 can recite most of the statistics off the 1986 and 1987 Topps Baseball Cards. I think I'm your man.
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.
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.
Is the answer potato?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.
sounds like a binomial distribution. mean = np
variance = np(1-p)
eta: google “example 7.17: the smith college diploma problem - SAS and R”
This is for a class in R.R is far, far better than SASS
Not that I'm aware of.Is there not a package for this....my knowledge about R is in the geostatistics side
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.
Do spouses count?I'm Indian so basically I am the winner of this thread unless there's a Korean amongst HORT.
It’s always 42.The answer is 42.
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.
That's more textbook math that I'm up for dealing with this week...😨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.
Was never good at story problems so could you expand on the 69?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'm Indian so basically I am the winner of this thread unless there's a Korean amongst HORT.
I assume dot not feather.I'm Indian so basically I am the winner of this thread unless there's a Korean amongst HORT.
This is what happens when you go to grad school in your mid-40s. Undergrad statistics was a long, long time ago. lolThat's more textbook math that I'm up for dealing with this week...😨
Had I known this was "textbook" problems, I'd have passed.This is what happens when you go to grad school in your mid-40s. Undergrad statistics was a long, long time ago. lol
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.