Manuals/calci/HYPGEOMDIST

HYPGEOMDIST(samples,numbersample,populations,numberpopulation)

• $samples$ is the sample's success.
• $numbersample$ is the sample's size.
• $populations$ is population's success.
• $numberpopulation$ 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.
• $numbersample$ is the total number of items in the sample.
• $populations$ is the number of items in the population that are classified as successes and $numberpopulation$ 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 $n$ individuals is selected without replacement in such a way that each subset of 
  size $n$ is equally likely to be chosen.

• The Hyper geometric probability distribution is:

${\frac {{\binom {m}{x}}{\binom {N-M}{n-x}}}{\binom {m}{x}}}$ for $x$ is an integer satisfying $max(0,n-N+M)<=x<=min(n,M)$. where $x$ is sample's success.

• $n$ is the sample's size.
• $M$ is population's success and $N$ 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.$samples<0$ or samples is greater than the smaller value of numbersample or populations.
3.$samples$ is less than the bigger of 0 or(numbersample-numberpopulation+populations)
4.$numbersample\leq 0$ or $numbersample>numberpopulation$
5.$populations\leq 0$ or  $populations>numberpopulation$ or $numberpopulation\leq 0$

ZOS Section

• The syntax is to calculate HYPGEOMDIST in ZOS is $HYPGEOMDIST(samples,numbersample,populations,numberpopulation)$
  • $samples$ is the sample's success.
  • $numbersample$ is the sample's size.
  • $populations$ is population's success.
  • $numberpopulation$ is the population size.
• For e.g.,HYPGEOMDIST(2..3,6..7,9..10,20)

Hyper-geometric Distribution

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

• BINOMDIST
• COMBIN
• FACT

References

Hypergeometric Distribution