Manuals/calci/BINOMDIST

From ZCubes Wiki
Revision as of 22:38, 18 November 2013 by Abin (talk | contribs) (→‎Description)
Jump to navigation Jump to search
BINOMDIST (ns, ts, ps, cu)


  • 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 ns} is the number of successes in trials.
  • 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 ts}  is the number of independent trials.
  • 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 ps}  is the probability of success on each trial
  • 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 cu} is a logical value that determines the form of the function.

Description

This function gives the individual element Binomial Distribution Probability.We can use this function when the following conditions are satisfied:

  1. A number of tests 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} should be fixed.
  2. Each test must be independent.
  3. Each test represents only two results(Success/Failure)
  4. No test has any impact on any other test.
For example, the number of ways to achieve 2 heads in a set of four tosses is "4 choose 2".
  • In BINOMDIST function, 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 ns} is the number of successes in trials.
  • TS is the number trials to be made, also 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 ns} 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 ts} should be integers.
  • 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 ps} is number of probability of success on each independent trials.
  • Finally 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 cu} is the logical value like TRUE or FALSE. If it is TRUE it will give the cumulative value or FALSE it will give the exact probability.

This function gives result as "Error" when

  1. 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 ns} and are not an Integer.
  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 ns,ts,ps} are not a numeric.
  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 ns < 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 ns > ts}
  4. Also 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 ps < 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 ps >1}

Example : =BINOMDIST (4, 12, 0.3, FALSE) is 0.2311

The binomial distribution with parameters n and p, we write 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 \tilde{} B(n, p)} . The probability of getting exactly 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 k } successes in 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 } trials is given by the Probability Mass Function: 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 b(k;n,p)=Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}} for k=0,1,2,3...n where \binom{n}{k} is the COMBIN(n,k) i.e.Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\binom {n}{k}}={\frac {n!}{k!(n-k)}}!}

The Cumulative Binomial 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 B(x;n,p) = Pr(X \le x) =\sum_{n=0}^x \binom{n}{i}p^{i}(1-p)^{(n-i)}}

Example

  1. Toss a coin for 12 times. What is the probability of getting exactly 7 heads.
    • Here NS=7,TS=12,and PS=1/2=0.5
    • BINOMDIST(7,12,0.5,FALSE)=0.193359375
  2. The LMB Company manufactures tires. They claim that only .007 of LMB tires are defective. What is the probability of finding 2 defective tires in a random sample of 50 LMB tires?
    • Here NS=2,TS=50 and PS=0.007
    • BINOMDIST(2,50,0.007,false)=0.0428446
Questions NS TS PS CU Result
Question 1 7 12 0.5(1/2) False 0.193359375
Question2 2 15 0.007 False 0.0428446

See Also

References

Binomial Distribution

Retrieved from "http://wiki.zcubes.com/index.php?title=Manuals/calci/BINOMDIST&oldid=195295"