R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> par2 = '0.5'
> par1 = '500'
> n <- as.numeric(par1)
> p <- as.numeric(par2)
> heads=rbinom(n-1,1,p)
> a=2*(heads)-1
> b=diffinv(a,xi=0)
> c=1:n
> pheads=(diffinv(heads,xi=.5))/c
> postscript(file="/var/www/html/rcomp/tmp/1mmuf1228224403.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op=par(mfrow=c(2,1))
> plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
> lines(c,b,col='red')
> lines(c,rep(0,n),col='black')
> plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
> lines(c,pheads,col='blue')
> lines(c,rep(.5,n),col='black')
> par(op)
> dev.off()
null device 
          1 
> b
  [1]   0  -1  -2  -3  -4  -5  -4  -3  -2  -3  -2  -1  -2  -1   0  -1   0   1
 [19]   0  -1  -2  -1   0  -1  -2  -1   0  -1  -2  -3  -4  -3  -4  -3  -2  -3
 [37]  -4  -3  -4  -3  -2  -3  -4  -5  -6  -7  -8  -7  -6  -7  -8  -7  -8  -7
 [55]  -8  -7  -6  -7  -8  -7  -8  -9  -8  -7  -6  -7  -6  -7  -6  -5  -6  -7
 [73]  -6  -5  -4  -5  -4  -3  -4  -5  -6  -7  -6  -7  -8  -9 -10  -9 -10  -9
 [91] -10 -11 -10 -11 -12 -13 -14 -15 -14 -15 -14 -13 -14 -13 -14 -13 -12 -13
[109] -14 -13 -12 -13 -14 -13 -12 -13 -12 -11 -10  -9  -8  -7  -8  -7  -8  -7
[127]  -8  -9 -10 -11 -12 -11 -12 -11 -12 -11 -12 -13 -12 -13 -14 -15 -16 -17
[145] -18 -17 -18 -17 -16 -15 -16 -17 -18 -17 -18 -17 -16 -17 -18 -19 -18 -17
[163] -18 -17 -16 -17 -18 -19 -18 -17 -16 -15 -14 -13 -14 -13 -12 -11 -10  -9
[181]  -8  -7  -8  -9 -10  -9 -10  -9 -10  -9  -8  -9 -10 -11 -10 -11 -10  -9
[199] -10  -9 -10  -9 -10  -9 -10 -11 -12 -11 -10 -11 -12 -13 -14 -15 -14 -15
[217] -16 -15 -16 -17 -18 -19 -20 -19 -20 -21 -20 -19 -20 -19 -20 -21 -22 -23
[235] -24 -23 -24 -25 -26 -27 -26 -27 -28 -29 -30 -29 -28 -27 -28 -29 -30 -31
[253] -30 -29 -28 -29 -28 -27 -28 -27 -26 -27 -28 -27 -28 -27 -28 -27 -26 -25
[271] -26 -27 -28 -29 -28 -27 -26 -25 -26 -25 -24 -23 -24 -25 -24 -25 -26 -27
[289] -26 -25 -24 -23 -22 -23 -24 -25 -26 -25 -24 -23 -24 -23 -22 -23 -24 -23
[307] -24 -23 -24 -23 -24 -23 -24 -23 -22 -21 -22 -23 -24 -23 -22 -21 -22 -21
[325] -22 -21 -22 -23 -24 -23 -22 -23 -24 -23 -22 -21 -22 -21 -20 -21 -20 -19
[343] -20 -21 -22 -23 -22 -23 -24 -23 -24 -25 -24 -25 -26 -25 -26 -25 -26 -27
[361] -26 -27 -28 -27 -26 -27 -26 -27 -26 -27 -28 -29 -30 -31 -30 -31 -30 -29
[379] -30 -29 -30 -29 -28 -27 -28 -27 -28 -27 -26 -27 -28 -27 -28 -29 -30 -29
[397] -30 -29 -28 -29 -28 -27 -26 -25 -24 -25 -24 -25 -24 -25 -26 -27 -28 -29
[415] -30 -31 -32 -33 -32 -33 -32 -31 -32 -31 -32 -33 -32 -33 -34 -35 -36 -35
[433] -34 -33 -32 -31 -32 -31 -32 -31 -30 -29 -30 -31 -30 -29 -30 -29 -30 -29
[451] -28 -29 -28 -27 -26 -25 -24 -25 -24 -25 -24 -25 -26 -25 -26 -25 -24 -25
[469] -26 -27 -28 -27 -28 -29 -30 -31 -32 -33 -34 -33 -34 -33 -34 -35 -34 -33
[487] -34 -35 -36 -37 -38 -39 -38 -39 -38 -39 -38 -39 -38 -37
> x <- b
> postscript(file="/var/www/html/rcomp/tmp/221ml1228224403.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> r <- spectrum(x,main='Raw Periodogram')
> dev.off()
null device 
          1 
> r
$freq
  [1] 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024
 [13] 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042 0.044 0.046 0.048
 [25] 0.050 0.052 0.054 0.056 0.058 0.060 0.062 0.064 0.066 0.068 0.070 0.072
 [37] 0.074 0.076 0.078 0.080 0.082 0.084 0.086 0.088 0.090 0.092 0.094 0.096
 [49] 0.098 0.100 0.102 0.104 0.106 0.108 0.110 0.112 0.114 0.116 0.118 0.120
 [61] 0.122 0.124 0.126 0.128 0.130 0.132 0.134 0.136 0.138 0.140 0.142 0.144
 [73] 0.146 0.148 0.150 0.152 0.154 0.156 0.158 0.160 0.162 0.164 0.166 0.168
 [85] 0.170 0.172 0.174 0.176 0.178 0.180 0.182 0.184 0.186 0.188 0.190 0.192
 [97] 0.194 0.196 0.198 0.200 0.202 0.204 0.206 0.208 0.210 0.212 0.214 0.216
[109] 0.218 0.220 0.222 0.224 0.226 0.228 0.230 0.232 0.234 0.236 0.238 0.240
[121] 0.242 0.244 0.246 0.248 0.250 0.252 0.254 0.256 0.258 0.260 0.262 0.264
[133] 0.266 0.268 0.270 0.272 0.274 0.276 0.278 0.280 0.282 0.284 0.286 0.288
[145] 0.290 0.292 0.294 0.296 0.298 0.300 0.302 0.304 0.306 0.308 0.310 0.312
[157] 0.314 0.316 0.318 0.320 0.322 0.324 0.326 0.328 0.330 0.332 0.334 0.336
[169] 0.338 0.340 0.342 0.344 0.346 0.348 0.350 0.352 0.354 0.356 0.358 0.360
[181] 0.362 0.364 0.366 0.368 0.370 0.372 0.374 0.376 0.378 0.380 0.382 0.384
[193] 0.386 0.388 0.390 0.392 0.394 0.396 0.398 0.400 0.402 0.404 0.406 0.408
[205] 0.410 0.412 0.414 0.416 0.418 0.420 0.422 0.424 0.426 0.428 0.430 0.432
[217] 0.434 0.436 0.438 0.440 0.442 0.444 0.446 0.448 0.450 0.452 0.454 0.456
[229] 0.458 0.460 0.462 0.464 0.466 0.468 0.470 0.472 0.474 0.476 0.478 0.480
[241] 0.482 0.484 0.486 0.488 0.490 0.492 0.494 0.496 0.498 0.500

$spec
  [1] 4.078587e+02 1.721708e+02 6.421201e+02 1.031866e+03 1.752833e+02
  [6] 2.956886e+02 1.799105e+02 2.493389e+02 3.449054e+02 1.478761e+01
 [11] 8.693376e+01 3.253501e+01 2.243413e+01 5.074232e+00 8.040320e-01
 [16] 5.135501e+00 6.943604e+00 2.354422e+01 2.706656e+01 1.693392e+01
 [21] 6.249885e+00 8.901292e+00 1.233941e+01 9.072946e+00 1.471029e+01
 [26] 6.560054e+00 2.762077e+00 7.403990e+00 1.000325e+01 1.312201e+01
 [31] 4.851434e+00 8.991069e+00 5.047649e+00 1.322977e+00 9.044390e+00
 [36] 4.549486e+00 6.144180e+00 5.602550e-01 1.864091e+00 2.364438e+00
 [41] 3.127949e-01 8.787846e+00 4.992524e-02 1.484973e-01 9.059937e+00
 [46] 6.150451e+00 1.461174e+00 1.116709e+00 3.901584e+00 1.436894e+00
 [51] 2.250192e+00 4.587737e-01 3.194416e+00 1.419184e+00 1.036083e+00
 [56] 2.213806e+00 1.156913e+00 9.411263e-01 4.958326e-01 3.428202e+00
 [61] 1.026822e+00 1.962679e+00 2.127487e+00 7.345456e-01 1.421410e+00
 [66] 6.467458e+00 3.023326e+00 6.975364e-01 2.421773e-02 3.857935e+00
 [71] 3.323096e-02 2.262161e-01 5.123051e-01 3.069347e-01 2.293748e+00
 [76] 8.259448e-01 2.250343e-01 1.913320e+00 2.404155e-01 1.507013e+00
 [81] 8.568789e-01 6.513630e-01 5.181772e-01 2.885050e-05 1.970155e-01
 [86] 1.626551e-01 5.265361e-01 1.024723e+00 2.029106e+00 1.112806e+00
 [91] 1.745897e+00 9.004735e-02 3.048852e-01 2.809058e-01 3.288019e-01
 [96] 1.862741e-01 2.093383e+00 7.484710e-02 5.707792e-01 1.881018e-01
[101] 2.250379e-02 1.757758e-01 1.426155e+00 5.200778e-02 6.106009e-01
[106] 5.267041e-01 1.237918e+00 4.602079e-01 1.365911e-01 1.026719e-01
[111] 2.743629e-01 2.855041e+00 5.502095e-01 1.197037e-01 1.041369e-01
[116] 6.651413e-01 1.818962e-02 3.615828e-01 8.501131e-01 1.735306e+00
[121] 6.454085e-01 4.529399e-01 1.291281e-01 1.087517e-01 5.999872e-01
[126] 1.166052e-01 3.158739e-01 2.654446e-01 3.989484e-01 1.217324e+00
[131] 6.081845e-01 5.562801e-02 1.453598e-01 8.534502e-02 2.178551e-01
[136] 6.599603e-01 5.538314e-01 1.202216e+00 1.653921e-01 7.466239e-01
[141] 2.463003e-01 7.283347e-02 1.917886e-01 1.013554e+00 7.813246e-02
[146] 4.072864e-01 3.816401e-02 2.083608e-02 4.466665e-01 2.726755e-01
[151] 7.274123e-02 3.612663e-01 3.660696e-01 3.818259e-01 6.890465e-01
[156] 2.460257e-02 2.864665e-02 1.027333e-01 2.169371e-01 3.479422e-01
[161] 6.774734e-02 2.450290e-01 1.582367e-01 3.597029e-01 2.703245e-01
[166] 2.567549e-01 1.236300e+00 3.303941e-01 3.769248e-01 2.174645e-01
[171] 8.219335e-02 5.477164e-01 4.564516e-01 2.904085e-01 7.265144e-01
[176] 3.953803e-01 1.576516e-01 1.136124e-01 1.033494e+00 1.363726e-01
[181] 9.166616e-01 2.410421e-02 8.992198e-01 5.970319e-01 5.785568e-01
[186] 6.369354e-02 5.095382e-02 2.729782e-02 1.120946e+00 1.076494e+00
[191] 6.526448e-03 3.605464e-01 8.522454e-01 3.135563e-02 1.142786e-01
[196] 3.681473e-01 2.035388e-01 4.065088e-01 1.207762e-01 5.695893e-02
[201] 1.371626e-01 6.207917e-01 8.568035e-02 4.683058e-02 5.053549e-01
[206] 3.234824e-01 4.611351e-02 2.768666e-02 9.146179e-02 3.052830e-01
[211] 2.582122e-02 2.623654e-01 2.428316e-02 5.444207e-01 1.496298e-01
[216] 5.431782e-01 1.733185e-01 5.503159e-01 4.815898e-01 1.334543e-01
[221] 1.738151e-01 2.054994e-01 8.477854e-02 6.039956e-01 1.263123e-01
[226] 2.305922e-02 9.367383e-02 3.240441e-01 2.247530e-01 3.976699e-01
[231] 2.629825e-01 1.507217e-01 5.018919e-01 3.671674e-02 4.498321e-02
[236] 7.110686e-02 4.943105e-01 9.485032e-01 1.399985e-01 3.093440e-01
[241] 4.518221e-01 4.066677e-01 1.820861e-01 2.524181e-01 3.033701e-01
[246] 7.228329e-02 2.969345e-01 2.085777e-03 3.780680e-01 1.870732e+00

$coh
NULL

$phase
NULL

$kernel
NULL

$df
[1] 1.791590

$bandwidth
[1] 0.0005773503

$n.used
[1] 500

$orig.n
[1] 500

$series
[1] "x"

$snames
NULL

$method
[1] "Raw Periodogram"

$taper
[1] 0.1

$pad
[1] 0

$detrend
[1] TRUE

$demean
[1] FALSE

attr(,"class")
[1] "spec"
> postscript(file="/var/www/html/rcomp/tmp/3sx2v1228224403.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> cpgram(x,main='Cumulative Periodogram')
> dev.off()
null device 
          1 
> system("convert tmp/1mmuf1228224403.ps tmp/1mmuf1228224403.png")
> system("convert tmp/221ml1228224403.ps tmp/221ml1228224403.png")
> system("convert tmp/3sx2v1228224403.ps tmp/3sx2v1228224403.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.840   0.614   1.062