Difference between revisions of "Manuals/calci/HYPGEOMDIST"

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<div style="font-size:30px">'''HYPGEOMDIST(n1,n2,n3,n4)'''</div><br/>
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<div style="font-size:30px">'''HYPGEOMDIST(samples,numbersample,populations,numberpopulation)'''</div><br/> sample_s,number
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*<math>n1</math> is the sample's success.
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*<math>samples</math> is the sample's success.
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*<math>n2</math> is the sample's size.
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*<math>numbersample</math> is the sample's size.
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*<math>n3</math> is population's success.
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*<math>populations</math> is population's success.
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*<math>n4</math> is the population size.
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*<math>numberpopulation</math> is the population size.
  
 
==Description==
 
==Description==
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*A Hypergeometric random variable is the number of successes that result from a Hypergeometric experiment.  
 
*A Hypergeometric random variable is the number of successes that result from a Hypergeometric experiment.  
 
*The probability distribution of a Hypergeometric random variable is called a Hypergeometric Distribution.
 
*The probability distribution of a Hypergeometric random variable is called a Hypergeometric Distribution.
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*In  HYPGEOMDIST(n1,n2,n3,n4) where n1 is the number of items in the Sample  that are classified as successes.  
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*In  HYPGEOMDIST(samples,numbersample,populations,numberpopulation) where samples is the number of items in the Sample  that are classified as successes.  
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*<math>n2</math> is the total number of items in the sample.
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*<math>numbersample</math> is the total number of items in the sample.
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*<math>n3</math> is the number of items in the population  that are classified as successes and <math>n4</math> is the total number of items in the sample.  
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*<math>populations</math> is the number of items in the population  that are classified as successes and <math>numberpopulation</math> is the total number of items in the sample.  
 
*The following conditions are applied to the Hypergeometric distribution:  
 
*The following conditions are applied to the Hypergeometric distribution:  
 
  1.This distribution is applies to sampling without replacement from a finite population whose elements can be
 
  1.This distribution is applies to sampling without replacement from a finite population whose elements can be
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*This function will give result as error when  
 
*This function will give result as error when  
 
  1.Any one of the argument is non-numeric.
 
  1.Any one of the argument is non-numeric.
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  2.<math>n1 < 0</math> or n1 is greater than the smaller value of n2 or n3.
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  2.<math>samples < 0</math> or samples is greater than the smaller value of numbersample or populations.
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  3.<math>n1</math> is less than the bigger of 0 or(n2-n4+n3)
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  3.<math>samples</math> is less than the bigger of 0 or(numbersample-numberpopulation+populations)
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  4.<math>n2 \le 0</math> or <math>n2>n4</math>
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  4.<math>numbersample \le 0</math> or <math>numbersample>numberpopulation</math>
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  5.<math>n3 \le 0</math> or  <math>n3>n4</math> or <math>n4 \le 0</math>
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  5.<math>populations \le 0</math> or  <math>populations>numberpopulation</math> or <math>numberpopulation \le 0</math>
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==ZOS Section==
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*The syntax is to calculate HYPGEOMDIST in ZOS is <math>HYPGEOMDIST(samples,numbersample,populations,numberpopulation)</math>
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**<math>samples</math> is the sample's success.
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**<math>numbersample</math> is the sample's size.
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**<math>populations</math> is population's success.
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**<math>numberpopulation</math> is the population size.
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*For e.g.,HYPGEOMDIST(2..3,6..7,9..10,20)
  
 
==Examples==
 
==Examples==

Revision as of 03:12, 18 June 2014

HYPGEOMDIST(samples,numbersample,populations,numberpopulation)


sample_s,number

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle samples} is the sample's success.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbersample} is the sample's size.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle populations} is population's success.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numberpopulation} is the population size.

Description

  • This function gives the result of Hypergeometric Distribution.
  • This distribution is a discrete probability distribution which is contrast to the binomial distribution.
  • A Hypergeometric random variable is the number of successes that result from a Hypergeometric experiment.
  • The probability distribution of a Hypergeometric random variable is called a Hypergeometric Distribution.
  • In HYPGEOMDIST(samples,numbersample,populations,numberpopulation) where samples is the number of items in the Sample that are classified as successes.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbersample} is the total number of items in the sample.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle populations} is the number of items in the population that are classified as successes and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numberpopulation} is the total number of items in the sample.
  • The following conditions are applied to the Hypergeometric distribution:
1.This distribution is applies to sampling without replacement from a finite population whose elements can be
classified into two categories like Success or Failure.
2.The population or set to be sampled consists of N individuals, objects,or elements 
3.Each individual can be  success (S) or a failure (F), and there are M successes in the population.
4.A sample of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
 individuals is selected without replacement in such a way that each subset of 
  size Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
 is equally likely to be chosen.
  • The Hyper geometric probability distribution is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\binom{m}{x} \binom{N-M}{n-x}}{\binom{m}{x}}} for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is an integer satisfying Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle max(0, n-N+M)<=x<=min(n,M)} . where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is sample's success.

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is the sample's size.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} is population's success and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} is the population size.
  • Here we can give any positive real numbers.
  • Suppose we are assigning any decimals numbers it will change in to Integers.
  • This function will give result as error when
1.Any one of the argument is non-numeric.
2. or samples is greater than the smaller value of numbersample or populations.
3.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle samples}
 is less than the bigger of 0 or(numbersample-numberpopulation+populations)
4.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbersample \le 0}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbersample>numberpopulation}

5.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle populations \le 0}
 or  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle populations>numberpopulation}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numberpopulation \le 0}

ZOS Section

  • The syntax is to calculate HYPGEOMDIST in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle HYPGEOMDIST(samples,numbersample,populations,numberpopulation)}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle samples} is the sample's success.
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbersample} is the sample's size.
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle populations} is population's success.
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numberpopulation} is the population size.
  • For e.g.,HYPGEOMDIST(2..3,6..7,9..10,20)

Examples

  1. Draw 6 cards from a deck without replacement.What is the probability of getting two hearts?
Here M = 13 number of hearts
N = 52 total number of cards
so N-M= 52-13= 39 and 
x=2,n=6 so n-x=6-2=4
=HYPGEOMDIST(2,6,13,52)=0.315129882
  1. 42 balls are numbered 1 - 42.You select six numbers between 1 and 42. What is the probability that they contain (i)match 3, (ii) match 4
(i)Here M= 6,N=42,x=3and n=6
HYPGEOMDIST(3,6,6,42)=0.02722185
(ii)Here M= 6,N=42,x=4and n=6
HYPGEOMDIST(4,6,6,42)=0.001801446

See Also

References

Hypergeometric Distribution

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