Continuous probability distribution.html (4314B)
1 <?xml version="1.0" encoding="UTF-8"?> 2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3 <html><head><link rel="stylesheet" href="sitewide.css"><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/><meta name="exporter-version" content="Evernote Mac 7.6 (457297)"/><meta name="altitude" content="-4.231714248657227"/><meta name="author" content="Alex Balgavy"/><meta name="created" content="2018-12-16 00:44:23 +0000"/><meta name="latitude" content="52.30035400390625"/><meta name="longitude" content="4.98817026635058"/><meta name="source" content="desktop.mac"/><meta name="updated" content="2018-12-16 01:27:45 +0000"/><title>Continuous probability distribution</title></head><body><h1>Continuous probability distribution</h1><h2>Normal distribution</h2><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">Notation:</div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;"><span style="font-size: 16px;"> 4 <img src="Continuous%20probability%20distribution.resources/6EA63762-9823-494B-9DD3-1623E3226929.png" height="20" width="95"/></span><br/></div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">Percentile rules:</div><ul><li><div>68%: within one standard deviation from mean</div></li><li><div>95%: within two standard deviations from mean</div></li><li><div>99.7%: within three standard deviations from mean</div></li></ul><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">To find 5 <img src="Continuous%20probability%20distribution.resources/97D6FF41-BFE0-4FAC-A44E-A37D3A25BC97.png" height="16" width="60"/>:</div><ol><li><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">Find z score for x:</div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;"><span style="font-size: 16px;"> 6 <img src="Continuous%20probability%20distribution.resources/F5864D1C-0372-40B3-B8ED-6183687DA8E5.png" height="31" width="69"/></span><br/></div></li><li style=""><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">Look up the cumulative probability for z.</div></li><li style=""><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;"> 7 <img src="Continuous%20probability%20distribution.resources/2F7F0CC9-0E00-43EB-BCDA-0440E725BE36.png" height="16" width="136"/>. So that’s your answer.</div></li></ol><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">Z scores come from distribution 8 <img src="Continuous%20probability%20distribution.resources/D01B4919-6913-4897-A0C3-FD8809571DF8.png" height="16" width="71"/></div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">Also:</div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;"><span style="font-size: 16px;"> 9 <img src="Continuous%20probability%20distribution.resources/D9A79AAB-2E2B-4D2A-B10D-BAA9DE2DCC39.png" height="18" width="187"/></span><br/></div><h3>Central limit theorem</h3><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">If you take sample size 10 <img src="Continuous%20probability%20distribution.resources/F9C40EC3-A503-48D4-BB6A-9BA2A98D78B1.png" height="13" width="41"/>, sample mean has approx normal distribution:</div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;"><span style="font-size: 16px;"> 11 <img src="Continuous%20probability%20distribution.resources/70078989-8600-4CFE-9E4E-7164D0773ED4.png" height="24" width="101"/></span><br/></div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">useful sometimes: 12 <img src="Continuous%20probability%20distribution.resources/EA4BF44C-A90C-434D-A8A9-ED2F5ED756CB.png" height="38" width="73"/></div><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;">If the population is already normally distributed, the sample is always normally distributed for any n.</div><h3>How do you know if something is normal?</h3><div style="margin-top: 1em; margin-bottom: 1em;-en-paragraph:true;"><div>Use a QQ plot. Put sample quantiles on y axis, theoretical quantiles on x axis.</div><div> 13 If there’s a linear correlation, sample is normal.</div><div> 14 In general, you can use QQ plots to compare two distributions/samples.</div></div><div><br/></div></body></html>