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Line 1: − + + + − '''RANDOMNUMBERGENERATION'''(Number, RandomNumber, Distribution, NewTableFlag, ProbabilityValue,Trials) − + + + + + + + + + + + + + + + + + + + + + − '''Number '''- represents the number of variables.+ + + + + + − '''RandomNumber '''- represents the number of random number+ + + − '''Distribution '''- represents the distribution method(i.e binomial) to create random values.+ − − '''NewTableFlag''' - is the TRUE or FALSE.If set as TRUE,the result in new sheet. If NewTableFlag is omitted, it assumed to be FALSE. − − '''ProbabilityValue '''- represents the probability value and should be in range 0 to 1. − − '''Trails''' - represents the number of trials. − − </div> − ---- − <div id="1SpaceContent" class="zcontent" align="left">The frequency distribution of the probability of a specified number of successes is an arbitrary number of repeated independent Bernoulli trials.</div> − ---- − <div id="7SpaceContent" class="zcontent" align="left"> − − Lets see an example in (Column1Row1) − − <nowiki>=RANDOMNUMBERGENERATION(3, 4, "Binomial", TRUE, 0.5)</nowiki> − − RANDOMNUMBERGENERATION returns the result in new sheet(9Space). − − <nowiki>=RANDOMNUMBERGENERATION(5, 4, "Binomial", TRUE, 0.3, -1)</nowiki> − − RANDOMNUMBERGENERATION returns the #ERROR(Trails < 0). − − </div> − ---- − <div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left"> − − RANDOM NUMBER GENERATION : BINOMIAL − − </div></div> − ---- − <div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div> − ---- − <div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div> − ---- − <div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div> − ---- − <div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div> − ---- − <div id="8SpaceContent" class="zcontent" align="left"> − − If Number < 0 or RandomNumber < 0, RANDOMNUMBERGENERATION returns the #ERROR. − − RANDOMNUMBERGENERATION returns the #ERROR, if Trails < 0. − − </div> − ---- − <div id="5SpaceContent" class="zcontent" align="left"> − − {| id="TABLE1" class="SpreadSheet blue" − |+ Random Number Generation<br />Binomial Distribution − |- class="even" − | 0 − | 1 − | 1 − |- class="odd" − | 1 − | 0 − | 2 − |- class="even" − | 0 − | 2 − | 1 − |- class="odd" − | 1 − | 1 − | 1 − |} − − </div> − ---- − <div id="2SpaceContent" class="zcontent" align="left"> − − {| id="TABLE3" class="SpreadSheet blue" − |+ Default Calci − |- class="even" − | class=" " | − | Column1 − | Column2 − | Column3 − | Column4 − |- class="odd" − | class=" " | Row1 − | class="sshl_f" | 9Space − | class=" " | − | class=" " | − | class=" " | − |- class="even" − | class=" " | Row2 − | class=" " | − | class=" " | − | class=" " | − | class=" sshl_f " | − |- class="odd" − | Row3 − | class=" " | − | class=" " | − | class=" " | − | class=" sshl_f " | − |- class="even" − | class=" " | Row4 − | class="sshl_f" | #ERROR − | class=" " | − | class=" " | − | class=" " | − |- class="odd" − | class=" " | Row5 − | class=" SelectTD1 ChangeBGColor SelectTD1" | − <div id="2Space_Handle" class="zhandles" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="2Space_Copy" class="zhandles" title="Click and Drag over to AutoFill other cells."></div><div id="2Space_Drag" class="zhandles" title="Click and Drag to Move/Copy Area.">[[Image:copy-cube.gif]] </div> − | class=" " | − | class=" " | − | class=" " | − |- class="even" − | Row6 − | class=" " | − | class=" " | − | class=" " | − | class=" " | − |} − − {| − | <span align="left">[[Image:calci1.gif]]</span> − | − | − [[Image:bold.gif]] − | − [[Image:italic.gif]] − | − [[Image:normal.gif]] − | − [[Image:underline.gif]] − | − [[Image:border.gif]] − | − [[Image:numbers.gif]] − | − [[Image:sort.gif]] − | − [[Image:formatcells.gif]] − | − [[Image:graphs.gif]] − | $ − |} − − </div> − ---- − <div id="9SpaceContent" class="zcontent" align="left"> − − {| class="SpreadSheet blue" − |+ Random Number Generation<br />Binomial Distribution − |- class="even" − | 0 − | 0 − | 0 − |- class="odd" − | 1 − | 1 − | 3 − |- class="even" − | 1 − | 1 − | 3 − |- class="odd" − | 0 − | 0 − | 1 − |} − − </div> − ----
no edit summary
<div id="6SpaceContent" class="zcontent" align="left">
<div style="font-size:30px">'''BINOMIAL(n,k)'''</div><br/>
*<math>n</math> is the number of items.
*<math>k </math> is the number of selection.
where,
==Description==
*This function gives the coefficent of the binomial distribution.
*Binomial coefficient is the set of positive integer which equals the number of combinations of k items that can be selected from a set of n items.
*The coefficients satisfy the Pascals recurrence.
*The binomial coefficents are denoted by <math>\binom{n}{k}</math> and it is read by n choose k.
*It is the coefficient of the <math>x^k</math> term in the polynomial expansion of the binomial thorem <math>(1 + x)^n</math>.
*The coefficient is occur in the formula of binomial thorem:
<math>(x+y)^n=\sum _{k=0}^n \binom{n}{k} x^{n-k} y^k</math> ,where <math> k\le n</math>.
*To find the coefficient of the binomial ,we can use several methods.
1. Recursive formula
2. Multiplicative formula
3. Factorial formula.
*1.Recursive Formula:
<math>\binom{n}{k}= \binom{n-1}{k-1} +\binom{n-1}{k}</math> for <math>n,k>0</math> and <math>1\le k\le n-1</math>.
*2. Multiplicative formula:
<math>\binom{n}{k}= \prod_{i=1}^k \frac{n+1-i}{i}</math>
*3.Factorial formula:
<math>\binom{n}{k}= \frac{n!}{k!(n-k)!}</math> where <math>k\le n</math>,and which is zero when <math>k>n</math>.
*Also for the initial values <math> \binom{n}{0}=\binom{n}{n}=1 </math> for <math>n\ge 0</math>.
*Most compact formula for the coefficient of the binomial value is Factorial formula.
*Factorial formula is symmetric of the combination formula.
==Examples==
#=BINOMIAL(10,3)= 120
#=BINOMIAL(20,7)= 77520
#=BINOMIAL(15,0)= 1
#=BINOMIAL(12,12)=1
#=BINOMIAL(1,-1) = 0
==See Also==
*[[Manuals/calci/BINOMDIST | BINOMDIST ]]
*[[Manuals/calci/BINOMIALDISTRIBUTED | BINOMIALDISTRIBUTED ]]
==References==