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GANCHROW lurks

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Ganch must be back, no one else posts integrals on gambling forums.

[frac=n]n+1[/frac] is of course correct, just as hhsilver has quite cleverly intuited.

No clue why mathdotcom gave him such a hard time.

But just for shits and giggles, a rather informal late night mathematical proof might read something like this:

We're looking for the E(sup(Xk)) where Xk is a vector of k realizations from the uniform distribution.

For the degenerate case of k=1, the pdf(sup(X1)) = pdf(X1) = 1. Hence:
[int=0]1||E(sup(X1)) = ||p dp[/int]
= [frac=1]2[/frac] * p[sup]2[/sup] | p=0 [hcc]rarr[/hcc] 1
= [frac=1]2[/frac]

So E(sup(X1)) = E(X1) = [frac=1]2[/frac]

For k=2:
Pr(sup(X2) = p [hcc]isin[/hcc] [0,1] )
= Pr( (x(1) [hcc]le[/hcc] p AND x(2) = p) OR (x(1) = p AND x(2) [hcc]le[/hcc] p) ) (this is the key step)
[hcc]asymp[/hcc] 2*p*[hcc]Delta[/hcc]​
Hence:
[int=0]1||E(sup(X2)) = ||2p[sup]2[/sup] dp[/int]
= [frac=2]3[/frac] * p[sup]3[/sup] | p=0 [hcc]rarr[/hcc] 1
= [frac=2]3[/frac]
Continuing with the same logic, it's clear that for k=n:

Pr(sup(Xn) = p ∈ [0,1] )
[hcc]asymp[/hcc] n*p[sup]n-1[/sup]*[hcc]Delta[/hcc]
[int=0]1||E(sup(Xn)) = ||n*p[sup]n[/sup] dp[/int]
= [frac=n]n+1[/frac] * p[sup]n+1[/sup] | p=0 [hcc]rarr[/hcc] 1
= [frac=n]n+1[/frac]​

QED​

Nicely done, hh. YOu get full credit in my book. :)
 
un fukin real

boys I am going with San Diego +1.5 tonight, and I am going big. You laugh, but check this out:


Hits+OBSP^x*(.4 - (x + HR/9))^int(E^10/12X+Y^2)*K=1*-4^s(PR(2))fract(x)divsup(9-x)


I know, who cares right? But:


AVG(nomdist(X+.24)-temp(*Q^3dist(4))-Qcalc(k/x^log5)logx

So

Hfactor((^$&^%*)(^#@$) +2 will give you a line about 12% off from WA numbers!!

boys trust me
 
perl -e "print grep ord $_,map{y/)!#@'%{];/0-8/;y/,0-9/--/c;s/[^0-9-]//g;$x.=qq~+$_~;chr eval $x;}q<Steve],'John Walker'@h`#nW1 SBR_;,,,'Loshak@@o'%EoG1er%DozerRX`1#Ricky_P@eROCK1@|`;#r';l#1CHALK1@Ax_{a`]{c')k#%,er#,wx;JJ_y{tWo1@&`;1FOUR_#@the end>=~m#([^\|&*\\ a-z]+)#gi#tr/-0-9//d;JenBird Long Live Tow! print RBS trixtrix Dozer Walker;"

:surrender:
 
LOL! What is he doing there Durito? What does it all mean? I'm entirely to dumb to even take a stab at it. Does it mean something, Durito??

I like how he tells the dood to post his question in the thread and if he finds it interesting, he might answer it. :lmao:

What a dick.