pathetic

So I'm stuck at my mom's work for the course of two hours. I have with me a book I've been telling myself to read for the past year and a pack of cards. Suddenly, I get a craving for something mathematical. So I devise a chi squared test to see if I had all the cards in my pack. Later I relalized that I failed two of the major assumptions:

That my sample size was less than 10% of the entire population, and
That it was a Simple Random Sample of the population (though I did shuffle really well, I tought)

Though I did make sure each expected cell count was _> 5

SO I shuffled really well and made 6 chi squaed tests of 4 groups, so df= 4-1 = 3, and the total number of each sample was 20 cards, based on the formula X^2 = E((o-e)^2/e) these were my actual results. They go in order H, D, C, S

[expected cell count is: 5 5 5 5]

1 6 2 11, X^2 = 12.4
8 0 8 4, X^2= 8.8
8 5 5 2, 3.8
6 6 5 3, 1.2
6 5 4 5 , 0.4
3 6 7 4, 2.0

Todd, I hope you're taking notes since this is practically ALL of chapter 12 right in front of you.

Though I haven't bothered to find the p values yet, though I'd suspect I may reject H0 on the first one @ a= .95

Whoops! I almost forgot:
H0= pi1= pi2= pi3 =pi4 = .25
HA: Ho is false

So then I went into wondering how likely it actually IS to get exactly 5 of each card, so I began experimenting with (quadronial?) expansion (a+b+c+d)^20, etc. As I went through sample sets without a calculator, I came upon something really cool, thogh it's probably been well documented and whatnot

YOU CAN DO A 3-D PASCAL'S TRAINGLE, and it works with the expansion of (a+b+c)^n, and the sum of all the coefficients is 3^n, as opposed to 2^n. So I started drawing it out, and it uses a 2-D Pascal's triangle as its sides and for the inner number you add the 3 numbers above it. I just think its's so cool. I wish I could draw one on the computer to show y'all, but you can draw it out by yourself.

Also, thanks to my handy dandy TI-89, I hope to actually find the probabnly of 5 of each card by doing (.25heart + .25 club + .25 spade + .25diammond) ^20 and finding the coeffcient with all 5 in it.