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Chris Losinger wrote: it's been a long time since i had to do this stuff, and i can't figure out how to solve what seems like it should be a simple calculation...
you have 6000 marbles in a box. 300 of them are black, the rest are white. you draw ten marbles without replacement.
what are the odds that three of the marbles you draw are black ?
Hi Chris, I think you want the hypergeometric probability distribution for this problem. This will give you the probability that in a sample of n objects drawn from a population, k will be black (no replacement).
Let:
N = 6000 be the total number of marbles <br />
n = 10 be the number of marbles drawn (your sample)<br />
B = 300 be the number of black marbles <br />
k = 3 be the number you are interested in
Then the probability of having k black marbles in a sample n of the total population N where f() is the probability, is:
f(k;N,B,n) = (B choose k) * ( (N-B) choose (n-k) ) / ( N choose n)
That is, there are N choose n total samples without replacement and B choose k ways to choose k black marbles and N-B choose n-k remaining ways to select.
Hope that helps.
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It's been a while, what's choose again? Is that like: a choose b = a!/b!
Logifusion[^]
If not entertaining, write your Congressman.
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Dustin Metzgar wrote: It's been a while, what's choose again? Is that like: a choose b = a!/b!
Almost, it's a choose b = a!/[b!(a-b)!].
--
Marcus Kwok
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My dumb-dumb Stats 100 textbook says that you can approximate the answer by using the binomial probability distribution.
Conditions:
1. The procedure has a fixed number of trials (10)
2. The trials must be independent.*
3. Each trial must have all outcomes classified into two categories (black and white).
4. The probabilities must remain constant for each trial.
n = # of trials = 10
x = # of successes among n trials = 3
p = prob. of success in any one trial = 300/6000 = 0.05
q = prob. of failure in any one trial = (1 - p) = 0.95
Then
P(3) = (10!) / ((10 - 3)! * 3!) * (0.05)^3 * (0.95)^(10-3)
Which, when I calculated it out, equals 0.0104750594. My TI's binompdf function agrees.
Stats/Math nerds, if this is wrong, please let us know.
* The justification for using this as an approximation even though we're selecting without replacement is this:
"When sampling without replacement, the events can be treated as if they were independent if the sample size is no more than 5% of the population size. (That is, n <= 0.05N.)" 10 <= 300, so we're good.
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Nice solution Jon. I didn't even think of that and sent the poor guy towards the hypergeometric distribution. Then I forgot he had to evaluate these huge factorials... 
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Last day I learned something about Fourier series.
how we can use it in actual application? what's the purpose of the same in computer programming area? I heard that it is used in graphics filters and all. Could you please add some more points on it?
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I haven't worked with Fourier Series or Transforms but according to this wiki article[^], it looks like it has many potential applications in computer programming.
Also, take a look around at mathworld[^] if you haven't already 
too much daily WTF for someone... - Anton AfanasyevLast modified: Sunday, August 20, 2006 1:04:07 PM --
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Fourier Series/Transforms have some interesting properties. One of the reasons that the FFT is so popular is because of those properties. You can grade a photo based on "sharpness" by looking at the output of the FFT, because of that you can actually provide focus "grading" as well as "grading" of atmospheric distortion. FFT and its output allows a great deal of information in evaluating noise vs. clarity, fuzziness vs. sharpness, etc.
read the article suggested above and do some google searches.
_________________________
Asu no koto o ieba, tenjo de nezumi ga warau.
Talk about things of tomorrow and the mice in the ceiling laugh. (Japanese Proverb)
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fourier series just like laplace transforms forms an important foundation in digital signal processing(DSP). Devices such as mobile phones, digital cameras, signal analysers, heart monitoring devices all use DSP and some aspect of fourier series is utilised. Look at the JPEG image compression thats based on discrete cosine transform (a type of fourier series), i think from memory.
Fourier series is a fascinating aspect of maths. I totally enjoyed it when I was going engineering mathematics a long time ago at uni.
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Do you know how we can program this using C++ or C?
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yes, the internet has plenty examples...
even on CP : FFT[^] for example...
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danx toxy 
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I saw the example. the GUI can be more user friendly
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still criticising...
the GUI is just a matter or representation, not a matter of calculation 
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and what about this[^] ???
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toxcct wrote:
and what about this[^] ???
sigview sure looks nice
too much daily WTF for someone... - Anton Afanasyev
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Reliable Software[^] has a couple of neat articles and examples in their freeware and science sections.
"I know which side I want to win regardless of how many wrongs they have to commit to achieve it." - Stan Shannon
Web - Blog - RSS - Math - LinkedIn
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In addition to DSP and other engineering fields, Fourier analysis has equally important applications in many science fields. Here I list some from my experience:
1) Atmospheric science: weather prediction, global wraming
2) Geophysics: ancient climatology, glacial analysis
3) Ocean science: wave analysis, surge prediction
4) Radio physics: spectral analysis
5) Computer science: data compression, pattern recognition
Best,
Jun
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Dear Jun
Thanks for your reply. even if we know the areas where there Fourier series used, it's hard to understand in what sense it helping to solve the problems. for eg.
Jun Du wrote: Computer science: data compression, pattern recognition
how it solves the problems in the quoted domain?
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Firstly, you need to understand the concepts of fourier series. Secondly, you need to then to have a thorough understanding of the domain you are interested in. Only then you will understand how concepts of fourier series can be used to solve problems.
If you are truly interested in fourier etc, then my recommendation will be to download a DSP pdf book from Analog Devices titled "The Scientist & Engineer's Guide to Digital Signal Processing". This is a great book and any DSP engineer will recommend it. Just ask Eric Jaccobson. Here is the URL:
http://www.analog.com/processors/learning/training/dsp_book_index.html
My other recommendation will be to learn matlab to gain an understanding in programming aspects of fourier series. This was the best way I had learnt fourier, laplace transforms etc.
My final recommendation will be to get yourself a engineering mathematics book i.e. Advanced Engineering Mathematics by Peter O'Neil here is a link: http://www.amazon.com/gp/product/0534400779/102-2429887-6445756?v=glance&n=283155 I have used this book and its an excellent reference in learning fourier laplace etc.
I dont want to sound harsh but to learn fourier requires dedication and it wont happen via osmosis nor will it happen overnight.
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thanks for your reply.
actually I'm studying about Fourier series as part of my exams.
so I wanted to get some detailed information on same. yea I heard that image processing, video filters are all based on Fourier series
but your replies are something more informative.
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ekynox wrote: I dont want to sound harsh but to learn fourier requires dedication and it wont happen via osmosis nor will it happen overnight.
As a side note to his comment, I would recommend learning their mathematical properties prior to learning their applications. If you understand what the series (be it Fourier or Laplace) does for you mathematically, you won't have any problem understanding a specific application of it.
If you decide to become a software engineer, you are signing up to have a 1/2" piece of silicon tell you exactly how stupid you really are for 8 hours a day, 5 days a week
Zac
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Sarath,
Ekynox has posted a great answer. As you know, Fourier is just one of the spectral analytical methods used in science and engineering. Other frequently used ones include Laplace, wavelet, etc. Learning Fourier Analysis is not hard at all, but knowing when, where and how to apply it to certain problems is. This demands proper domain knowledge and experience.
As a trivial example, take pattern recognition (PR). With PR, we often need to compare a 2D data array with the reference so that we can find similarities or differences of the two patterns. Using Fourier analysis, instead of compare the raw data directly, we can change to compare a selected set of wave components. Thus, by reducing the amount of data we need to compare, we can speed up the PR significantly.
Similar applications in data compression (DC). By expanding to Fourier series, we can (approximately) represent the original data set by less amount of data (wave component coefficients).
Best,
Jun
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