Manuals/calci/HYPGEOMDIST

HYPGEOMDIST (sample_s,number_sample,population_s,number_population,cumulative)

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 number sample} 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 population s} 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 number population} 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 (sample_s,number_sample,population_s,number_population,cumulative) 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 number sample} 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.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 < 0}
 or samples is greater than the smaller value of numbersample or populations.
3.  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

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 sample s} 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 number sample} 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 population s} 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 number population} is the population size.
For e.g.,HYPGEOMDIST(2..3,6..7,9..10,20)

Hyper-geometric Distribution

Examples

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

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

References

Hypergeometric Distribution

List of Main Z Functions

Z3 home

Manuals/calci/HYPGEOMDIST

Contents

Description

ZOS

Examples

Related Videos

See Also

References