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# Hypergeometric distribution

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Imagine you have a large bag full of skittles of X different colors. There are n skittles in total. In the bag there are n1 skittles of one specific color, n2 of another color, n3 of yet another and so on until nx skittles of the last color.

Imagine you stick your hand into the bag without looking, and draw k skittles at random. You now want to know the probability of getting k1 skittles of the first color, k2 skittles of colur number two, and so forth until kskittles of color number X. I think the answer should be:

P(A) = [ ∏(from i = 1 to X) (nC ki) ]/ (n C k)

Or, (if shown correctly on the computer screen):

X

P(A)  =    ∏ (nC ki)       /

i = 1           /    (n C k)

Is this written correctly, or have I made a mistake somewhere?

Guest Nov 23, 2014

#5
+5

I used the capital pi notation, which workes the same way as sigma notation, except that one uses products, not sums:

∏(i=1 to 5) 2i = 2*4*6*8*10 = 3840

So, after some trying and failing:

$$P(A) =\displaystyle \;\;\frac{Pi \limits_{n=1}^X\ ^{n{_i}}C_{k_i}}{^nC_k}$$

I'm really not able to write ∏ in the formula :(

Anyway, I really hope it's written correctly :)

Guest Nov 23, 2014
Sort:

#1
+91436
+5

This is all too much for me at the moment but I would try using known quatities of things.

If I could work out what to do for the known quatities then I would extrapolate to get a formula for the unknown quanities.

I am not saying it will necessarily work but that is how I would try to attack the problem.

good luck

Melody  Nov 23, 2014
#2
+91436
+5

As far as notation goes I think that this is what you are after?

$$P(A)=\displaystyle \lim_{i=1}^X}\;\;\frac{^{n{_i}}C_{k_i}}{^nC_k}$$

this is written in LaTex. I opened the LaTex formula button and typed in

P(A)=\displaystyle \lim_{i=1}^X}\;\;\frac{^{n{_i}}C_{k_i}}{^nC_k}

Melody  Nov 23, 2014
#3
+17711
+5

Shouldn't each of the individual factors in your product have this form?

(n-sub-i C k-sub-i) · (n minus n-sub-i C k minus k-sub-i) / n C k

geno3141  Nov 23, 2014
#4
+91436
0

Beats me - i havent even thought about it and if i did it may not help much. :)

I just reproduced what was there.

Melody  Nov 23, 2014
#5
+5

I used the capital pi notation, which workes the same way as sigma notation, except that one uses products, not sums:

∏(i=1 to 5) 2i = 2*4*6*8*10 = 3840

So, after some trying and failing:

$$P(A) =\displaystyle \;\;\frac{Pi \limits_{n=1}^X\ ^{n{_i}}C_{k_i}}{^nC_k}$$

I'm really not able to write ∏ in the formula :(

Anyway, I really hope it's written correctly :)

Guest Nov 23, 2014
#6
+91436
0

Oh ok   Thanks

I have not seen capital pi used like that before.

Melody  Nov 23, 2014

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