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<div class="headertitle"><div class="title">binomial_dist.cpp</div></div>
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<a href="../../d6/db0/binomial__dist_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"><a class="line" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813"> 22</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(<span class="keywordtype">double</span> n, <span class="keywordtype">double</span> p) { <span class="keywordflow">return</span> n * p; }</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861"> 29</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(<span class="keywordtype">double</span> n, <span class="keywordtype">double</span> p) { <span class="keywordflow">return</span> n * p * (1 - p); }</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span></div>
<div class="foldopen" id="foldopen00036" data-start="{" data-end="}">
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc"> 36</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(<span class="keywordtype">double</span> n, <span class="keywordtype">double</span> p) {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">return</span> std::sqrt(<a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>}</div>
</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span></div>
<div class="foldopen" id="foldopen00047" data-start="{" data-end="}">
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a"> 47</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(<span class="keywordtype">double</span> n, <span class="keywordtype">double</span> r) {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordtype">double</span> numerator = n;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordtype">double</span> denominator = r;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= ((n - r) + 1); i--) {</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> numerator *= i;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> }</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; r; i++) {</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> denominator *= i;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">return</span> numerator / denominator;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span>}</div>
</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span></div>
<div class="foldopen" id="foldopen00065" data-start="{" data-end="}">
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"><a class="line" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76"> 65</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(<span class="keywordtype">double</span> n, <span class="keywordtype">double</span> p, <span class="keywordtype">double</span> x) {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, x) * std::pow(p, x) * std::pow(1 - p, n - x);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>}</div>
</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span></div>
<div class="foldopen" id="foldopen00074" data-start="{" data-end="}">
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"><a class="line" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25"> 74</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(<span class="keywordtype">double</span> n, <span class="keywordtype">double</span> p, <span class="keywordtype">double</span> lower_bound,</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordtype">double</span> upper_bound) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">double</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> = 0;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower_bound; i &lt;= upper_bound; i++) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> += <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, i) * std::pow(p, i) * std::pow(1 - p, n - i);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a>;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>}</div>
</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span></div>
<div class="foldopen" id="foldopen00084" data-start="{" data-end="}">
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="../../d6/db0/binomial__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 84</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> std::cout &lt;&lt; <span class="stringliteral">&quot;expected value : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(100, 0.5)</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> std::cout &lt;&lt; <span class="stringliteral">&quot;variance : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(100, 0.5) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> std::cout &lt;&lt; <span class="stringliteral">&quot;standard deviation : &quot;</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(100, 0.5) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> std::cout &lt;&lt; <span class="stringliteral">&quot;exactly 30 successes : &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(100, 0.5, 30)</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> std::cout &lt;&lt; <span class="stringliteral">&quot;45 or more successes : &quot;</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> &lt;&lt; <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(100, 0.5, 45, 100) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> </div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span>}</div>
</div>
<div class="ttc" id="abinomial__dist_8cpp_html_a19ae0a6a2bd200fd1eb0e31b2bf4cc76"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a></div><div class="ttdeci">double binomial_x_successes(double n, double p, double x)</div><div class="ttdef"><b>Definition</b> <a href="#l00065">binomial_dist.cpp:65</a></div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_a4416a7bc7fa87201883c54cdc4c82813"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a></div><div class="ttdeci">double binomial_expected(double n, double p)</div><div class="ttdef"><b>Definition</b> <a href="#l00022">binomial_dist.cpp:22</a></div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_a76ed6ce71415fb400b65f0656cef3d25"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a></div><div class="ttdeci">double binomial_range_successes(double n, double p, double lower_bound, double upper_bound)</div><div class="ttdef"><b>Definition</b> <a href="#l00074">binomial_dist.cpp:74</a></div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_a78d36635232e54b5d71fcbf1eac9a49a"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a></div><div class="ttdeci">double nCr(double n, double r)</div><div class="ttdef"><b>Definition</b> <a href="#l00047">binomial_dist.cpp:47</a></div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_acd4dd4558031e4c5d045c801f73d8861"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a></div><div class="ttdeci">double binomial_variance(double n, double p)</div><div class="ttdef"><b>Definition</b> <a href="#l00029">binomial_dist.cpp:29</a></div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00084">binomial_dist.cpp:84</a></div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_af09e51f513cee647d41192ab0a872cdc"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a></div><div class="ttdeci">double binomial_standard_deviation(double n, double p)</div><div class="ttdef"><b>Definition</b> <a href="#l00036">binomial_dist.cpp:36</a></div></div>
<div class="ttc" id="anamespaceprobability_html"><div class="ttname"><a href="../../d4/ded/namespaceprobability.html">probability</a></div><div class="ttdoc">Probability algorithms.</div></div>
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