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Functions</h2></td></tr>
<tr class="memitem:a4416a7bc7fa87201883c54cdc4c82813" id="r_a4416a7bc7fa87201883c54cdc4c82813"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a> (double n, double p)</td></tr>
<tr class="memitem:a4416a7bc7fa87201883c54cdc4c82813" id="r_a4416a7bc7fa87201883c54cdc4c82813"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a> (double n, double p)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<td class="memname">double binomial_expected </td>
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<td class="memname">double binomial_range_successes </td>
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<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
<div class="line"><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"><span class="lineno"> 77</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower_bound; i &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a>; i++) {</div>
<div class="line"><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) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - i);</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> += <a class="code hl_function" href="#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - i);</div>
<div class="line"><span class="lineno"> 79</span> }</div>
<div class="line"><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"><span class="lineno"> 81</span>}</div>
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<tr>
<td class="memname">double binomial_standard_deviation </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
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</dl>
<dl class="section return"><dt>Returns</dt><dd>\(\sigma = \sqrt{\sigma^2} = \sqrt{n\cdot p\cdot (1-p)}\) </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 36</span> {</div>
<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(<a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(<a class="code hl_function" href="#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
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<tr>
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<td class="memname">double binomial_x_successes </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>n</em>, </td>
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<p>calculates the probability of exactly x successes </p><dl class="section return"><dt>Returns</dt><dd>\(\displaystyle P(n,p,x) = {n\choose x} p^x (1-p)^{n-x}\) </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 65</span> {</div>
<div class="line"><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) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - x);</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - x);</div>
<div class="line"><span class="lineno"> 67</span>}</div>
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<tr>
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<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
<div class="line"><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;expected value : &quot;</span> &lt;&lt; <a class="code hl_function" href="#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(100, 0.5)</div>
<div class="line"><span class="lineno"> 86</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 87</span> </div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;variance : &quot;</span> &lt;&lt; <a class="code hl_function" href="#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(100, 0.5) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;standard deviation : &quot;</span></div>
<div class="line"><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; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 91</span> &lt;&lt; <a class="code hl_function" href="#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(100, 0.5) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 92</span> </div>
<div class="line"><span class="lineno"> 93</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"><span class="lineno"> 93</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;exactly 30 successes : &quot;</span> &lt;&lt; <a class="code hl_function" href="#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(100, 0.5, 30)</div>
<div class="line"><span class="lineno"> 94</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 95</span> </div>
<div class="line"><span class="lineno"> 96</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;45 or more successes : &quot;</span></div>
<div class="line"><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; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 97</span> &lt;&lt; <a class="code hl_function" href="#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(100, 0.5, 45, 100) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 98</span> </div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 100</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></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> binomial_dist.cpp:65</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> binomial_dist.cpp:22</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> binomial_dist.cpp:74</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> binomial_dist.cpp:36</div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_a19ae0a6a2bd200fd1eb0e31b2bf4cc76"><div class="ttname"><a href="#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> binomial_dist.cpp:65</div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_a4416a7bc7fa87201883c54cdc4c82813"><div class="ttname"><a href="#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a></div><div class="ttdeci">double binomial_expected(double n, double p)</div><div class="ttdef"><b>Definition</b> binomial_dist.cpp:22</div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_a76ed6ce71415fb400b65f0656cef3d25"><div class="ttname"><a href="#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> binomial_dist.cpp:74</div></div>
<div class="ttc" id="abinomial__dist_8cpp_html_af09e51f513cee647d41192ab0a872cdc"><div class="ttname"><a href="#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a></div><div class="ttdeci">double binomial_standard_deviation(double n, double p)</div><div class="ttdef"><b>Definition</b> binomial_dist.cpp:36</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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Here is the call graph for this function:</div>
@@ -417,19 +380,12 @@ Here is the call graph for this function:</div>
<tr>
<td class="memname">double nCr </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>n</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>n</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>r</em>&#160;</td>
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<tr>
<td></td>
<td>)</td>
<td></td><td></td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>r</em></span>&#160;)</td>
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@@ -466,7 +422,7 @@ Here is the call graph for this function:</div>
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