Balls2

*To*: mathgroup at smc.vnet.net*Subject*: [mg31366] Balls2*From*: "Juan Erfá" <erfa11 at hotmail.com>*Date*: Wed, 31 Oct 2001 03:30:56 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello. In my letter from yesterday there is a fail. The function F2 shoud be: F2[b_,x_]:=Sort[F[b,x],Greater], and not Sort[F1[b,x],Greater] The function F, is define dawn in the page and it have to be in the begining. The all letter shoud be like that: << DiscreteMath`Combinatorica` The problen is how to share b balls in x boxes. There is 4 cases: In[1]:= F[b_, x_] := (q = Table[0, {x}]; Table[r = Random[Integer, {1, x}]; q[[r]]++, {b}]; q) 1.The balls are equals, the boxes are diferent In[2]:= F1[b_,x_]:=RandomComposition[b,x] 2.The balls are equals, the boxes are equals In[3]:= F2[b_,x_]:=Sort[F[b,x],Greater] 3.The balls are diferents, the boxes are equals In[4]:= F3[b_, x_] := (a3 = F2[b, x]; r3 = RandomTableau[a3]; PadRight[r3, x, {{}}]) 4.The balls are diferents, the boxes are diferents In[5]:= F4[b_, x_] := (a4 = F3[b, x]; r4 = RandomPermutation[x]; Map[a4[[#]] &, r4]) In[6]:= F1[11,7] Out[6]= {0,2,0,3,5,1,0} In[7]:= F2[11,7] Out[7]= {5,2,2,1,1,0,0} In[8]:= F3[11,7] Out[8]= {{1,4,6,11},{2,5},{3,8},{7,9},{10},{},{}} In[9]:= F4[11,7] Out[9]= {{2,6},{3},{10},{},{1,4,5,7,9,11},{},{8}} I have also calculate the probability to share b balls in x boxes, and n balls at least in one box. In[12]:= Prob[b_, x_, n_] := (t = Table[F[b, x], {200}]; c = Count[Map[MemberQ[#, n] &, t], True]; 0.005*c) The birthday problem is: In[13]:= Prob[23,365,2] Out[18]= 0.515 I get this results: In[14]:= Prob[90,365,3] Out[14]= 0.515 In[15]:= Prob[190,365,4] Out[20]= 0.505 The function BN[x_,n_,p_]= b, (to get b, knowing x, n, and the probability p) If n=2, then p=1-x!/((x-b)! x^b), and we can solve this ecuation for b In[23]:= B2[x_,p_]:=FindRoot[1-x!/((x-b)!x^b)==p,{b,1,x}] In[24]:= B2[365,.5] Out[24]= {b->22.7677} If n>2, then I don't know. Salutes.Juan PD.I don't know how to pas the programs I write in Mathematica to the e-mail, so I have to copy and paste every sentens, an after to correct the signs that can not be convert, and I get confuse. _________________________________________________________________ Descargue GRATUITAMENTE MSN Explorer en http://explorer.msn.es/intl.asp