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.
- HYPGEOMDIST(),returns the hypergeometric distribution.
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.
- 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.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
- 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 (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 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)
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
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References