Notes on the Central Limit Theorem
<h1>Theory</h1>
<p>Let <em>Xᵢ</em> with <em>i</em> = {1 … <em>n</em>} be <em>n</em> random variables (r.v.), independently distributed with distributions D<em>ᵢ</em> not necessarily identical, but with the same mean <em>μ</em> and variance <em>σ</em>².</p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:383/1*I43WcRXtsNw5gdVuC26NmQ.png" style="height:40px; width:383px" /></p>
<p>(1)</p>
<p>Let us define the “<em>sum</em>” r.v. <em>Sₙ</em></p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:456/1*6rcLsvDWAqBL-1_QBJoqdw.png" style="height:86px; width:456px" /></p>
<p>(2)</p>
<p>By the linearity property of the expected value</p>
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