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Ehiz
Member Since Jul 26th, 2007

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Math problem: Average winning roll {WoW}

Dec 21st 2009 1:43PM I found this journal article. http://www.math.wm.edu/~leemis/2006informsjoc.pdf

There is a formula for the E(X sub r) where r is the r-th ordered statistic. This is on page 6 of 12 on the left hand side and it is the first equation

So in this case
n=5, (Number of samples drawn)
r=5, (The 5th ordered stat or in this case the winning roll)
p=.01,
q= 1-p = .99

(p is basically the probability of choosing a specific number since in our case it is uniform the probability of choosing any number is equal to .01)

j=0 (Now I believe this is number of number above r. In other words if we wanted to take a look at the expected value of the lowest number then j=4 since there are 4 numbers above the lowest...I think not 100% sure on this)

Ok, going to try and number crunch this.

Math problem: Average winning roll {WoW}

Dec 21st 2009 12:51PM I have a BS degree in Probability and Statistics and currently working on my MS at the moment. Now I am not following either method as to why those are the answer.

First thing first is that you have a discrete uniform distribution from 1 to 100, (this takes care of the integer problem)

Next we are going to take 5 random draws from the discrete uniform distribution and only look at the maximum. So we want to find the distribution of the either the 5th ordered statistic or the Nth ordered statistic (I am getting hung up on this at the moment)

Now for a continuous uniform distribution the ordered statistics are distributed with a Beta distribution, but for discrete I do not know of the top of my head.

So we are looking for the expected value (average) of the the maximum.

There is this http://en.wikipedia.org/wiki/German_tank_problem but that does not seem to answer the question that is asked.

Ahh, I am going to look more into this.