bernoullicharts/1_-_log_1_x_alt_series__bound.svg

<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Created with matplotlib (https://matplotlib.org/) -->
<svg height="345.6pt" version="1.1" viewBox="0 0 460.8 345.6" width="460.8pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
 <defs>
  <style type="text/css">
*{stroke-linecap:butt;stroke-linejoin:round;}
  </style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill:#ffffff;"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill:#ffffff;"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path d="M 0 0 
L 0 3.5 
" id="m7f3997a849" style="stroke:#000000;stroke-width:0.8;"/>
      </defs>
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="73.800255" xlink:href="#m7f3997a849" y="307.584"/>
      </g>
     </g>
     <g id="text_1">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 73.800255, 322.182437)" x="73.800255" y="322.182437">0.0</text>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="138.744153" xlink:href="#m7f3997a849" y="307.584"/>
      </g>
     </g>
     <g id="text_2">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 138.744153, 322.182437)" x="138.744153" y="322.182437">0.2</text>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="203.688051" xlink:href="#m7f3997a849" y="307.584"/>
      </g>
     </g>
     <g id="text_3">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 203.688051, 322.182437)" x="203.688051" y="322.182437">0.4</text>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="268.631949" xlink:href="#m7f3997a849" y="307.584"/>
      </g>
     </g>
     <g id="text_4">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 268.631949, 322.182437)" x="268.631949" y="322.182437">0.6</text>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="333.575847" xlink:href="#m7f3997a849" y="307.584"/>
      </g>
     </g>
     <g id="text_5">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 333.575847, 322.182437)" x="333.575847" y="322.182437">0.8</text>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="398.519745" xlink:href="#m7f3997a849" y="307.584"/>
      </g>
     </g>
     <g id="text_6">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 398.519745, 322.182437)" x="398.519745" y="322.182437">1.0</text>
     </g>
    </g>
    <g id="text_7">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 236.16, 335.860562)" x="236.16" y="335.860562">Input Coin's Heads Probability (λ)</text>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path d="M 0 0 
L -3.5 0 
" id="m1310e2269d" style="stroke:#000000;stroke-width:0.8;"/>
      </defs>
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#m1310e2269d" y="295.49341"/>
      </g>
     </g>
     <g id="text_8">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 299.292628)" x="50.6" y="299.292628">0</text>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#m1310e2269d" y="249.464983"/>
      </g>
     </g>
     <g id="text_9">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 253.264202)" x="50.6" y="253.264202">1</text>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#m1310e2269d" y="203.436557"/>
      </g>
     </g>
     <g id="text_10">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 207.235775)" x="50.6" y="207.235775">2</text>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#m1310e2269d" y="157.40813"/>
      </g>
     </g>
     <g id="text_11">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 161.207349)" x="50.6" y="161.207349">3</text>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#m1310e2269d" y="111.379704"/>
      </g>
     </g>
     <g id="text_12">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 115.178922)" x="50.6" y="115.178922">4</text>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#m1310e2269d" y="65.351277"/>
      </g>
     </g>
     <g id="text_13">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 69.150496)" x="50.6" y="69.150496">5</text>
     </g>
    </g>
    <g id="text_14">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-90, 38.157812, 174.528)" x="38.157812" y="174.528">Coin Flips Needed</text>
    </g>
   </g>
   <g id="line2d_13">
    <path clip-path="url(#p3f521644dd)" d="M 73.832727 249.471886 
L 77.112066 250.162448 
L 80.391405 250.840187 
L 83.670744 251.505562 
L 86.950083 252.159009 
L 90.229421 252.800952 
L 93.50876 253.431794 
L 96.788099 254.051925 
L 100.067438 254.661721 
L 103.346777 255.261541 
L 106.626116 255.851736 
L 109.905455 256.432638 
L 113.184793 257.004573 
L 116.464132 257.567853 
L 119.743471 258.122779 
L 123.02281 258.669642 
L 126.302149 259.208725 
L 129.581488 259.7403 
L 132.860826 260.264632 
L 136.140165 260.781976 
L 139.419504 261.29258 
L 142.698843 261.796685 
L 145.978182 262.294525 
L 149.257521 262.786325 
L 152.53686 263.272307 
L 155.816198 263.752685 
L 159.095537 264.227668 
L 162.374876 264.697458 
L 165.654215 265.162255 
L 168.933554 265.622252 
L 172.212893 266.077636 
L 175.492231 266.528594 
L 178.77157 266.975304 
L 182.050909 267.417944 
L 185.330248 267.856686 
L 188.609587 268.2917 
L 191.888926 268.723151 
L 195.168264 269.151204 
L 198.447603 269.576018 
L 201.726942 269.997752 
L 205.006281 270.416561 
L 208.28562 270.832598 
L 211.564959 271.246014 
L 214.844298 271.656959 
L 218.123636 272.06558 
L 221.402975 272.472024 
L 224.682314 272.876436 
L 227.961653 273.278958 
L 231.240992 273.679734 
L 234.520331 274.078905 
L 237.799669 274.476613 
L 241.079008 274.872999 
L 244.358347 275.268202 
L 247.637686 275.662362 
L 250.917025 276.055621 
L 254.196364 276.448118 
L 257.475702 276.839993 
L 260.755041 277.231388 
L 264.03438 277.622445 
L 267.313719 278.013306 
L 270.593058 278.404115 
L 273.872397 278.795017 
L 277.151736 279.186159 
L 280.431074 279.577687 
L 283.710413 279.969753 
L 286.989752 280.362507 
L 290.269091 280.756105 
L 293.54843 281.150701 
L 296.827769 281.546457 
L 300.107107 281.943533 
L 303.386446 282.342095 
L 306.665785 282.742312 
L 309.945124 283.144357 
L 313.224463 283.548406 
L 316.503802 283.954641 
L 319.78314 284.363246 
L 323.062479 284.774413 
L 326.341818 285.188337 
L 329.621157 285.605221 
L 332.900496 286.025271 
L 336.179835 286.448703 
L 339.459174 286.875737 
L 342.738512 287.306604 
L 346.017851 287.741539 
L 349.29719 288.180788 
L 352.576529 288.624605 
L 355.855868 289.073255 
L 359.135207 289.527011 
L 362.414545 289.986161 
L 365.693884 290.451 
L 368.973223 290.92184 
L 372.252562 291.399002 
L 375.531901 291.882826 
L 378.81124 292.373665 
L 382.090579 292.871887 
L 385.369917 293.377881 
L 388.649256 293.892051 
L 391.928595 294.414826 
L 395.207934 294.946652 
L 398.487273 295.488 
" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;"/>
   </g>
   <g id="line2d_14">
    <path clip-path="url(#p3f521644dd)" d="M 73.832727 249.464983 
L 77.112066 248.820585 
L 80.391405 248.360301 
L 83.670744 248.176187 
L 86.950083 247.623846 
L 90.229421 246.611221 
L 93.50876 246.703278 
L 96.788099 246.242993 
L 100.067438 245.414482 
L 103.346777 245.138311 
L 106.626116 244.125686 
L 109.905455 243.941572 
L 113.184793 243.021003 
L 116.464132 244.125686 
L 119.743471 242.560719 
L 123.02281 240.535468 
L 126.302149 240.995753 
L 129.581488 239.522843 
L 132.860826 240.995753 
L 136.140165 240.443412 
L 139.419504 240.903696 
L 142.698843 239.338729 
L 145.978182 238.694331 
L 149.257521 238.049933 
L 152.53686 236.484967 
L 155.816198 237.773763 
L 159.095537 235.748512 
L 162.374876 234.367659 
L 165.654215 235.656455 
L 168.933554 232.710636 
L 172.212893 234.735887 
L 175.492231 234.459716 
L 178.77157 230.225101 
L 182.050909 233.631204 
L 185.330248 231.513897 
L 188.609587 232.710636 
L 191.888926 228.844248 
L 195.168264 228.107793 
L 198.447603 226.266656 
L 201.726942 226.634884 
L 205.006281 225.438145 
L 208.28562 224.241405 
L 211.564959 221.571757 
L 214.844298 224.241405 
L 218.123636 222.124098 
L 221.402975 220.098847 
L 224.682314 219.178279 
L 227.961653 218.994165 
L 231.240992 219.454449 
L 234.520331 219.178279 
L 237.799669 215.864232 
L 241.079008 219.086222 
L 244.358347 215.680118 
L 247.637686 216.048346 
L 250.917025 212.826356 
L 254.196364 215.680118 
L 257.475702 214.115152 
L 260.755041 211.629617 
L 264.03438 207.210888 
L 267.313719 207.763229 
L 270.593058 208.131456 
L 273.872397 208.131456 
L 277.151736 202.608045 
L 280.431074 206.474433 
L 283.710413 204.449182 
L 286.989752 204.173012 
L 290.269091 196.348179 
L 293.54843 192.113564 
L 296.827769 196.716406 
L 300.107107 195.703781 
L 303.386446 196.808463 
L 306.665785 194.507042 
L 309.945124 192.942075 
L 313.224463 189.720086 
L 316.503802 186.037811 
L 319.78314 188.983631 
L 323.062479 182.815822 
L 326.341818 177.01624 
L 329.621157 179.962059 
L 332.900496 173.426023 
L 336.179835 170.57226 
L 339.459174 176.555956 
L 342.738512 173.518079 
L 346.017851 171.032544 
L 349.29719 167.442327 
L 352.576529 147.097763 
L 355.855868 150.96415 
L 359.135207 167.534384 
L 362.414545 148.846843 
L 365.693884 156.119334 
L 368.973223 130.895757 
L 372.252562 131.632211 
L 375.531901 127.949937 
L 378.81124 124.635891 
L 382.090579 104.383383 
L 385.369917 83.486477 
L 388.649256 70.782632 
L 391.928595 53.568 
L 395.207934 56.513819 
" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="text_15">
    <text style="font-family:DejaVu Sans;font-size:12px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 236.16, 35.472)" x="236.16" y="35.472">Coin Flips for 1 - log(1+x)</text>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 64.6 78.82825 
L 313.43125 78.82825 
Q 315.43125 78.82825 315.43125 76.82825 
L 315.43125 48.472 
Q 315.43125 46.472 313.43125 46.472 
L 64.6 46.472 
Q 62.6 46.472 62.6 48.472 
L 62.6 76.82825 
Q 62.6 78.82825 64.6 78.82825 
z
" style="fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;"/>
    </g>
    <g id="line2d_15">
     <path d="M 66.6 54.570437 
L 86.6 54.570437 
" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;"/>
    </g>
    <g id="line2d_16"/>
    <g id="text_16">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:start;" transform="rotate(-0, 94.6, 58.070437)" x="94.6" y="58.070437">Coin Flip Lower Bound (Mendo)</text>
    </g>
    <g id="line2d_17">
     <path d="M 66.6 69.248562 
L 86.6 69.248562 
" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;"/>
    </g>
    <g id="line2d_18"/>
    <g id="text_17">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:start;" transform="rotate(-0, 94.6, 72.748562)" x="94.6" y="72.748562">Avg. Coins Flipped 1 - log(1+x) (Alt. Series)</text>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p3f521644dd">
   <rect height="266.112" width="357.12" x="57.6" y="41.472"/>
  </clipPath>
 </defs>
</svg>