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/1iu2m1228298064.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  -6  -7  -8  -7  -8  -9  -8  -9 -10 -11 -12 -13
 [19] -12 -11 -12 -13 -12 -13 -14 -15 -14 -15 -16 -15 -16 -17 -18 -19 -18 -17
 [37] -18 -19 -20 -19 -18 -19 -18 -17 -16 -15 -16 -17 -18 -19 -20 -19 -20 -19
 [55] -20 -19 -18 -17 -18 -19 -18 -19 -20 -19 -20 -21 -20 -19 -18 -19 -20 -19
 [73] -18 -17 -18 -17 -18 -19 -18 -19 -20 -21 -22 -21 -20 -19 -18 -19 -20 -19
 [91] -20 -21 -20 -21 -22 -23 -24 -23 -24 -23 -24 -25 -26 -27 -26 -27 -26 -27
[109] -26 -27 -26 -25 -24 -25 -26 -27 -26 -25 -26 -25 -24 -23 -24 -25 -24 -23
[127] -24 -23 -24 -23 -22 -21 -22 -21 -22 -21 -22 -23 -24 -23 -24 -25 -24 -25
[145] -26 -27 -28 -27 -28 -29 -30 -31 -30 -31 -30 -31 -30 -29 -30 -31 -32 -31
[163] -30 -31 -30 -31 -30 -29 -30 -31 -30 -29 -28 -29 -30 -29 -28 -29 -28 -29
[181] -28 -27 -28 -29 -30 -29 -28 -29 -30 -29 -30 -31 -32 -33 -34 -33 -34 -35
[199] -34 -35 -34 -35 -36 -35 -36 -37 -36 -35 -34 -35 -34 -33 -34 -33 -32 -31
[217] -32 -33 -34 -33 -32 -33 -32 -33 -32 -31 -32 -31 -30 -31 -30 -29 -30 -31
[235] -30 -31 -30 -31 -30 -31 -30 -31 -32 -31 -32 -33 -32 -31 -30 -29 -30 -29
[253] -30 -31 -30 -29 -30 -31 -32 -33 -32 -33 -34 -33 -32 -31 -32 -33 -34 -35
[271] -34 -35 -34 -35 -36 -35 -34 -35 -36 -37 -38 -39 -38 -39 -38 -39 -40 -39
[289] -38 -39 -40 -39 -38 -39 -38 -39 -40 -41 -40 -41 -42 -43 -42 -41 -42 -43
[307] -44 -43 -42 -41 -42 -43 -42 -41 -40 -39 -38 -39 -38 -37 -38 -37 -36 -37
[325] -38 -37 -38 -39 -38 -37 -38 -39 -40 -39 -38 -37 -36 -37 -38 -37 -38 -39
[343] -38 -39 -38 -39 -38 -37 -38 -37 -38 -37 -38 -37 -38 -39 -38 -37 -38 -39
[361] -38 -37 -36 -35 -36 -35 -36 -37 -36 -35 -34 -35 -34 -35 -34 -35 -34 -33
[379] -34 -33 -32 -33 -34 -33 -34 -33 -32 -33 -32 -33 -32 -31 -30 -29 -30 -29
[397] -28 -29 -28 -27 -28 -27 -26 -25 -24 -23 -22 -23 -24 -23 -22 -23 -22 -23
[415] -22 -21 -20 -19 -20 -19 -20 -19 -20 -19 -20 -21 -22 -23 -24 -25 -24 -25
[433] -26 -25 -26 -25 -26 -25 -26 -25 -26 -27 -28 -29 -30 -31 -32 -31 -30 -31
[451] -30 -29 -28 -29 -28 -27 -28 -27 -26 -27 -28 -27 -26 -27 -26 -25 -24 -23
[469] -24 -23 -22 -21 -20 -21 -20 -21 -22 -23 -22 -21 -22 -21 -22 -21 -20 -21
[487] -20 -21 -22 -23 -24 -23 -24 -25 -26 -25 -26 -25 -24 -23
> x <- b
> postscript(file="/var/www/html/rcomp/tmp/2leq41228298064.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] 6.235321e+03 7.903437e+02 1.370404e+03 1.133253e+02 1.685680e+02
  [6] 1.842911e+02 1.694199e+02 5.857583e+00 1.962834e+02 2.248144e+02
 [11] 6.792495e+01 5.725780e+01 1.069768e+01 5.451190e+00 4.001714e+00
 [16] 1.107140e+00 2.609424e+00 6.217468e+00 5.451131e+00 6.371758e+00
 [21] 4.332373e+00 1.609534e+01 1.725951e+00 1.176685e+01 6.656182e+00
 [26] 1.338961e+00 2.967892e+00 2.122937e+00 1.531150e+01 4.891803e+00
 [31] 1.309108e-01 4.063637e+00 9.717222e+00 1.224885e+01 2.364386e-01
 [36] 8.877779e+00 9.647408e-01 1.299208e+00 6.010451e+00 2.986331e-01
 [41] 1.313878e+00 1.864747e+00 7.511770e-01 4.861426e+00 1.052347e+00
 [46] 6.744695e+00 2.718930e-01 1.356904e+00 1.508486e-01 8.650614e-01
 [51] 3.286736e-01 1.580255e+00 4.526562e-01 3.126677e-01 9.344989e-01
 [56] 3.127782e-01 1.519372e+00 4.656521e+00 2.126213e-01 7.158752e-01
 [61] 1.135970e+00 1.111465e+00 1.294100e+00 3.670277e-01 5.567457e-01
 [66] 8.060363e-01 3.726955e-01 5.177383e-02 7.643853e-01 2.992056e+00
 [71] 1.520984e-02 1.204206e+00 6.084260e-01 4.372636e+00 1.151074e-01
 [76] 6.645949e-01 2.646623e-01 1.590953e+00 1.573021e+00 7.825029e-01
 [81] 1.823925e-01 4.155060e-01 1.131809e+00 3.227512e-01 1.850701e-01
 [86] 1.462915e+00 5.122283e-01 1.063328e+00 1.620283e+00 1.962008e-01
 [91] 2.739317e+00 4.228022e-01 2.561365e+00 4.094941e-01 1.875659e+00
 [96] 1.021507e+00 3.248185e-01 4.370265e-01 2.681422e-01 3.133902e-01
[101] 5.027037e-01 2.233846e+00 1.004251e+00 6.274477e-02 6.452629e-01
[106] 5.199618e-01 1.958626e+00 4.339423e-01 6.550499e-01 3.190153e+00
[111] 7.339914e-01 4.409727e-01 1.606877e-01 9.353663e-01 5.038369e-01
[116] 4.136566e-01 2.574554e-01 2.163376e-02 7.671881e-02 2.894384e-01
[121] 2.776247e-02 4.831505e-01 1.976608e+00 2.972072e-01 1.012900e+00
[126] 4.310099e-01 1.846488e-01 5.047380e-01 3.694067e-01 4.886200e-02
[131] 5.280183e-01 2.739478e-01 4.519679e-01 9.509061e-01 2.861743e-01
[136] 7.743906e-01 6.110810e-02 8.915838e-02 8.019170e-01 3.413926e-01
[141] 8.089036e-01 3.038703e-01 1.026346e+00 5.168674e-01 5.562190e-01
[146] 3.454312e-02 1.081442e+00 1.232436e+00 4.082352e-01 1.610642e-01
[151] 5.649618e-02 2.507730e-01 1.083139e-01 5.060163e-01 2.078200e-01
[156] 3.542055e-02 5.205986e-02 6.771844e-01 6.477556e-02 1.882265e-01
[161] 3.503401e-01 6.528964e-01 1.302715e-01 5.888645e-01 3.976080e-01
[166] 3.826680e-01 5.989382e-01 5.002989e-01 2.227707e-01 1.173874e+00
[171] 1.610509e-01 8.230159e-01 1.008707e-02 1.729081e-01 1.529114e-03
[176] 1.313265e-01 4.164823e-01 3.333370e-01 4.079013e-01 4.146397e-01
[181] 7.263936e-01 2.639299e-03 6.335099e-02 2.008235e+00 1.725997e-01
[186] 1.638542e-01 2.885240e-01 2.083065e-01 7.704363e-02 1.390068e-01
[191] 2.088360e-01 7.081483e-01 2.739053e-02 5.157555e-01 3.410498e-01
[196] 3.050688e-01 4.308333e-01 2.329683e-01 5.141473e-02 5.644809e-02
[201] 8.481790e-03 6.162187e-02 1.186513e+00 1.024142e-02 3.754968e-02
[206] 1.167817e-01 3.486874e-01 1.579560e+00 8.197256e-02 5.657648e-03
[211] 5.776626e-01 1.869987e-02 1.656653e-01 5.187003e-01 2.030591e-01
[216] 1.593696e+00 8.820816e-02 1.626304e-01 2.376136e-01 4.354724e-01
[221] 1.691735e-01 2.335154e-01 2.555477e-01 1.125341e+00 9.345757e-03
[226] 3.045387e-02 6.060118e-01 4.557194e-01 9.437351e-02 3.761727e-02
[231] 7.779077e-02 2.816221e-01 1.190691e-01 1.381849e-01 3.662899e-01
[236] 4.477735e-02 3.123637e-01 4.695490e-01 2.263570e-01 6.852194e-02
[241] 2.635449e-01 5.016557e-01 5.897779e-01 3.121457e-03 4.528649e-01
[246] 8.386503e-02 6.494415e-03 1.475317e-01 3.421983e-01 5.593394e-03

$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/32sei1228298064.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/1iu2m1228298064.ps tmp/1iu2m1228298064.png")
> system("convert tmp/2leq41228298064.ps tmp/2leq41228298064.png")
> system("convert tmp/32sei1228298064.ps tmp/32sei1228298064.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.844   0.605   1.513