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create_matrix_triangular_simulate_Normal_Restricted.html
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<h1 id="create_matrix_triangular_simulate_normal_restricted">create_matrix_triangular_simulate_Normal_Restricted</h1>
<h2 id="ex-i">Ex I.</h2>
<h4 id="a-function-that-takes-a-square-matrix-and-sets-it-to-zero-above-the-main-diagonal">A
function that takes a square matrix and sets it to zero above the main
diagonal</h4>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>fun_tri_mat <span class="ot"><-</span> <span class="cf">function</span>(A){</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> D <span class="ot"><-</span> <span class="fu">dim</span>(A)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(D[<span class="dv">1</span>] <span class="sc">!=</span> D[<span class="dv">2</span>]) <span class="fu">stop</span>(<span class="st">"A must be square matrix"</span>)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a> n <span class="ot"><-</span> D[<span class="dv">1</span>]</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>(n<span class="dv">-1</span>)){</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span>(j <span class="cf">in</span> (i<span class="sc">+</span><span class="dv">1</span>)<span class="sc">:</span>n){</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a> A[i, j] <span class="ot"><-</span> <span class="dv">0</span></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(A)</span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>A <span class="ot"><-</span> <span class="fu">matrix</span>(<span class="dv">1</span>, <span class="dv">4</span>, <span class="dv">4</span>)</span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a>A</span></code></pre></div>
<pre><code>## [,1] [,2] [,3] [,4]
## [1,] 1 1 1 1
## [2,] 1 1 1 1
## [3,] 1 1 1 1
## [4,] 1 1 1 1</code></pre>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>A2 <span class="ot"><-</span> <span class="fu">fun_tri_mat</span>(A)</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>A2</span></code></pre></div>
<pre><code>## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 1 1 0 0
## [3,] 1 1 1 0
## [4,] 1 1 1 1</code></pre>
<hr />
<h2 id="ex-ii">EX II.</h2>
<h4 id="a-function-that-is-a-normal-sample-of-the-given-limits-in-such-a-way-that-the-simulated">A
function that is a normal sample of the given limits, in such a way that
the simulated</h4>
<h4 id="values-must-be-larger-than-the-specified-value-of-a-and-smaller-than-the-specified-value-of-b">values
must be larger than the specified value of A and smaller than the
specified value of B.</h4>
<h4 id="in-this-function-the-size-of-the-production-sample-and-the-users-desired-mean-and-standard-deviation">In
this function, the size of the production sample and the user’s desired
mean and standard deviation,</h4>
<h4 id="as-well-as-the-users-desired-limits-are-given-in-the-function-arguments">as
well as the user’s desired limits, are given in the function
arguments.</h4>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>create_normal_restrict <span class="ot"><-</span> <span class="cf">function</span>(size, </span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>Mu, Sig, a, b){</span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a> i <span class="ot">=</span> <span class="dv">0</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a> Sample <span class="ot"><-</span> <span class="fu">c</span>()</span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">while</span>(i <span class="sc"><=</span> size){</span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a> temp1 <span class="ot"><-</span> <span class="fu">rnorm</span>(<span class="dv">1</span>, Mu, Sig)</span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(temp1 <span class="sc"><</span> b <span class="sc">&&</span> temp1 <span class="sc">></span> a){</span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a> i <span class="ot">=</span> i <span class="sc">+</span> <span class="dv">1</span>; Sample[i] <span class="ot"><-</span> temp1</span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(Sample)</span>
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a>s <span class="ot"><-</span> <span class="fu">create_normal_restrict</span>(<span class="at">size =</span> <span class="dv">10</span>, <span class="at">Mu =</span> <span class="dv">0</span>, <span class="at">Sig =</span> <span class="dv">2</span>, <span class="at">a =</span> <span class="dv">2</span>, <span class="at">b =</span> <span class="dv">4</span>)</span>
<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a>s</span></code></pre></div>
<pre><code>## [1] 2.243753 2.141859 2.499287 2.411613 2.786077 3.007454 2.016532 2.194721
## [9] 2.960471 3.566795 3.004377</code></pre>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">all</span>(s <span class="sc">></span> <span class="dv">2</span>) <span class="sc">&&</span> <span class="fu">all</span>(s <span class="sc"><</span> <span class="dv">4</span>)</span></code></pre></div>
<pre><code>## [1] TRUE</code></pre>
<hr />
<h2 id="ex-iii">EX III.</h2>
<h4 id="edit-code-for-ex-ii">Edit code for EX II.</h4>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>create_normal_restrict <span class="ot"><-</span> <span class="cf">function</span>(size, </span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>Mu, Sig, a, b){</span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a> Sample <span class="ot"><-</span> <span class="fu">c</span>()</span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>size){</span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a> temp1 <span class="ot"><-</span> <span class="fu">rnorm</span>(<span class="dv">1</span>, Mu, Sig)</span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a> <span class="cf">while</span>(temp1 <span class="sc"><</span> a <span class="sc">||</span> temp1 <span class="sc">></span> b){</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a> temp1 <span class="ot"><-</span> <span class="fu">rnorm</span>(<span class="dv">1</span>, Mu, Sig)</span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a> Sample[i] <span class="ot"><-</span> temp1</span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(Sample)</span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a>s <span class="ot"><-</span> <span class="fu">create_normal_restrict</span>(<span class="at">size =</span> <span class="dv">20</span>, <span class="at">Mu =</span> <span class="dv">2</span>, <span class="at">Sig =</span> <span class="dv">3</span>, <span class="at">a =</span> <span class="dv">3</span>, <span class="at">b =</span> <span class="dv">5</span>)</span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a>s</span></code></pre></div>
<pre><code>## [1] 3.911585 3.921723 3.122110 3.948795 4.774382 3.076863 3.469231 4.365678
## [9] 3.269514 4.202419 3.463050 3.377031 3.380355 3.799234 4.243608 4.837978
## [17] 3.189766 4.140438 3.525532 3.183216</code></pre>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">all</span>(s <span class="sc">></span> <span class="dv">3</span>) <span class="sc">&&</span> <span class="fu">all</span>(s <span class="sc"><</span> <span class="dv">5</span>)</span></code></pre></div>
<pre><code>## [1] TRUE</code></pre>
<hr />
<h2 id="ex-iv">EX IV.</h2>
<h4 id="simulation-to-prove-the-weak-law-of-large-numbers">Simulation to
prove the weak law of large numbers</h4>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>Weak_law_large_num <span class="ot"><-</span> <span class="cf">function</span>(size, Mu, <span class="at">showPlot =</span> <span class="cn">TRUE</span>){</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a> n <span class="ot"><-</span> size</span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a> E <span class="ot"><-</span> <span class="fu">list</span>()</span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>n){</span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a> E[[i]] <span class="ot"><-</span> <span class="fu">rnorm</span>(i, <span class="at">mean =</span> Mu, <span class="at">sd =</span> <span class="dv">1</span>)</span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a> E_mean <span class="ot"><-</span> <span class="fu">unlist</span>(<span class="fu">lapply</span>(E, mean))</span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a> list_result <span class="ot"><-</span> <span class="fu">list</span>(<span class="at">Mean_result =</span> E_mean, <span class="at">list_result =</span> E)</span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span>(showPlot){</span>
<span id="cb13-10"><a href="#cb13-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">plot</span>(<span class="at">x =</span> <span class="dv">1</span><span class="sc">:</span>n, <span class="at">y =</span> E_mean, <span class="at">col =</span> <span class="st">"darkblue"</span>, <span class="at">type =</span> <span class="st">"l"</span>, <span class="at">xlab =</span> <span class="st">"size of sample"</span>, <span class="at">ylab =</span> <span class="st">"Sample Mean"</span>)</span>
<span id="cb13-11"><a href="#cb13-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">abline</span>(<span class="at">h =</span> Mu, <span class="at">lwd =</span> <span class="fl">1.5</span>, <span class="at">lty =</span> <span class="dv">2</span>, <span class="at">col =</span> <span class="st">"yellow"</span>)</span>
<span id="cb13-12"><a href="#cb13-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">legend</span>(<span class="st">"topright"</span>, <span class="at">legend =</span> <span class="fu">expression</span>(mu), <span class="at">lty =</span> <span class="dv">2</span>, <span class="at">lwd =</span> <span class="dv">3</span>, <span class="at">col =</span> <span class="st">"yellow"</span>, <span class="at">bg =</span> <span class="st">"black"</span>, <span class="at">cex =</span> <span class="dv">3</span>, </span>
<span id="cb13-13"><a href="#cb13-13" aria-hidden="true" tabindex="-1"></a> <span class="at">text.col =</span> <span class="st">"white"</span>)</span>
<span id="cb13-14"><a href="#cb13-14" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb13-15"><a href="#cb13-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">return</span>(list_result)</span>
<span id="cb13-16"><a href="#cb13-16" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb13-17"><a href="#cb13-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb13-18"><a href="#cb13-18" aria-hidden="true" tabindex="-1"></a>Result <span class="ot"><-</span> <span class="fu">Weak_law_large_num</span>(<span class="at">size =</span> <span class="fl">1e+4</span>, <span class="at">Mu =</span> <span class="fl">2.5</span>, <span class="at">showPlot =</span> T) </span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>E <span class="ot"><-</span> Result<span class="sc">$</span>list_result</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>E[[<span class="dv">5</span>]]</span></code></pre></div>
<pre><code>## [1] 3.116940 4.857782 1.882710 1.226727 1.481583</code></pre>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>E[[<span class="dv">10</span>]]</span></code></pre></div>
<pre><code>## [1] 3.292993 2.268598 3.157134 3.571759 3.159709 1.713299 4.043080 3.037837
## [9] 2.692407 1.889819</code></pre>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>E[[<span class="dv">20</span>]]</span></code></pre></div>
<pre><code>## [1] -0.6664324 4.8782451 2.9060415 0.6526347 1.9626721 0.7180531
## [7] 3.2976689 3.4396635 1.9731405 2.4000012 1.4585400 3.0614244
## [13] 2.0365139 3.8850386 2.3145039 3.2419005 4.0532249 2.6540564
## [19] 2.6158590 3.2020568</code></pre>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>E[[<span class="dv">50</span>]]</span></code></pre></div>
<pre><code>## [1] 2.0276034 2.1878928 4.3126485 2.5441813 0.3146525 2.4537864 3.5692615
## [8] 3.7117593 0.9467995 2.6343303 0.5337894 2.4028012 1.1944789 2.2382669
## [15] 1.6622360 2.8248932 3.2131675 3.0547236 3.0619314 1.9556758 2.4052841
## [22] 2.4501912 1.2803878 2.2348861 1.8950170 2.2464262 0.9141530 2.1164518
## [29] 3.2233743 1.5031934 5.0491144 2.7211629 2.6247484 2.4374962 0.8734581
## [36] 2.7386009 1.3735067 1.2746713 0.8909878 2.0065375 2.0193940 0.4261524
## [43] 2.3482436 2.7726120 2.3382846 2.5743570 3.2558597 0.8673530 3.0893295
## [50] 1.3701027</code></pre>
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