http://learn.cemetech.net/index.php?title=TI-BASIC:Randnorm&feed=atom&action=history TI-BASIC:Randnorm - Revision history 2022-05-22T04:31:06Z Revision history for this page on the wiki MediaWiki 1.34.0 http://learn.cemetech.net/index.php?title=TI-BASIC:Randnorm&diff=681&oldid=prev Maintenance script: Initial automated import 2016-02-24T18:13:17Z <p>Initial automated import</p> <p><b>New page</b></p><div>{{Template:TI-BASIC:Command<br /> |picture=RANDNORM.GIF<br /> |summary=Generates a random normally-distributed number with specified mean and standard deviation.<br /> |syntax=randNorm(''µ'',''σ'',[''n''])<br /> |location=Press:<br /> # MATH to access the [[TI-BASIC:Math|Math]] menu.<br /> # LEFT to access the PRB submenu.<br /> # 6 to select randNorm(, or use arrows.<br /> |compatibility=TI-83/84/+/SE<br /> |size=2 bytes<br /> }}<br /> <br /> randNorm(''µ'',''σ'') generates a normally-distributed pseudorandom number with [[TI-BASIC:Mean|Mean]] ''µ'' and [[TI-BASIC:Stddev|standard deviation]] ''σ''. The result returned will most probably be within the range ''µ''±3''σ''. randNorm(''µ'',''σ'',''n'') generates a list of ''n'' normally-distributed pseudorandom numbers with mean ''µ'' and standard deviation ''σ''.<br /> <br /> ''seed''→rand affects the output of randNorm(.<br /> <br /> 0→rand<br /> 0<br /> randNorm(0,1)<br /> -1.585709623<br /> randNorm(0,1,3)<br /> {-1.330473604 1.05074514 -.0368606663}<br /> <br /> Although a theoretical normally distributed variable could take on any real value, numbers on a calculator have a limited precision, which leads to a maximum range of approximately ''µ''±7.02''σ'' for values of randNorm(.<br /> <br /> = Optimization =<br /> <br /> When the mean is 0 and the standard deviation 1, [[TI-BASIC:Invnorm|InvNorm(]]rand) and invNorm(rand(N)) save space over randNorm(0,1) and randNorm(0,1,N) respectively.<br /> <br /> = Formulas =<br /> <br /> The value of randNorm( for a given seed can be expressed in terms of [[TI-BASIC:Rand|Rand]]:<br /> <br /> <br /> randNorm(µ,σ)=µ-σinvNorm(rand<br /> <br /> <br /> This is identical to the output of randNorm( in the sense that for the same seed, both expressions will generate the same random numbers.<br /> <br /> The following formula can be used to get a target interval where A and B are two real intervals.<br /> <br /> <br /> µ=(A+B)/2<br /> σ=(-A+B)/6<br /> <br /> <br /> = Related Commands =<br /> <br /> * [[TI-BASIC:Rand|Rand]]<br /> * [[TI-BASIC:Randint|RandInt(]]<br /> * [[TI-BASIC:Randbin|RandBin(]]<br /> * [[TI-BASIC:Randm|RandM(]]<br /> * [[TI-BASIC:Randintnorep|randIntNoRep(]][[Category:TI-BASIC]]<br /> [[Category:TIBD]]</div> Maintenance script