<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: RANDOM_2:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Omega</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">Sigma</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">Omega</font><br/>  for <font color="Olive" title="b3">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b2">Sigma</font><br/>  for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b5">X</font> being   <a href="random_1.html#NM1" title="RANDOM_1:NM.1">Real-Valued-Random-Variable</a> of <font color="Olive" title="b2">Sigma</font>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">r</font> &amp; <font color="Olive" title="b5">X</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>  &amp; <font color="Olive" title="b5">X</font> <a href="random_1.html#R1" title="RANDOM_1:pred.1">is_integrable_on</a> <font color="Olive" title="b3">P</font> &amp; <span class="p1">(<span class="default"><a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Olive" title="b5">X</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> 2 <a href="mesfunc6.html#R2" title="MESFUNC6:pred.2">is_integrable_on</a>  <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Olive" title="b3">P</font> holds <br/><font color="Olive" title="b3">P</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b6">t</font> where <font color="Olive" title="b6">t</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">Omega</font> : <font color="Olive" title="b4">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b5">X</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Olive" title="b6">t</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="random_1.html#K8" title="RANDOM_1:func.8">expect</a> (<font color="Olive" title="b5">X</font>,<font color="Olive" title="b3">P</font>)</span>)</span></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> </span> } </span>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="random_2.html#K1" title="RANDOM_2:func.1">variance</a> (<font color="Olive" title="b5">X</font>,<font color="Olive" title="b3">P</font>)</span>)</span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">r</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> 2</span>)</span></div></div>
