Difference between revisions of "Manuals/calci/BINOMDIST"
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The binomial distribution with parameters n and p, we write <math> X \tilde{} B(n, p)</math>. | The binomial distribution with parameters n and p, we write <math> X \tilde{} B(n, p)</math>. | ||
The probability of getting exactly <math> k </math> successes in <math> n </math> trials is given by the Probability Mass Function: | The probability of getting exactly <math> k </math> successes in <math> n </math> trials is given by the Probability Mass Function: | ||
| − | <math> b(k;n,p) = Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}</math>,for k=0,1,2,3...n where (n,k)is the COMBIN(n,k) i.e.<math>(n,k)=\frac | + | <math> b(k;n,p) = Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}</math>,for k=0,1,2,3...n where (n,k)is the COMBIN(n,k) i.e.<math>(n,k)=\frac{n!}{k!(n-k)}!</math> |
| − | The Cumulative Binomial Ditrbution is:B(x;n,p)=Pr(X<=x) = | + | The Cumulative Binomial Ditrbution is:<math>B(x;n,p)</math> = <math>Pr(X<=x) =\sum_{n=0}^\x \binom{n}{i}p^{i}(1-p)^{(n-i)}</math> |
*It calculates the individual term Binomial Distribution Probability. | *It calculates the individual term Binomial Distribution Probability. | ||
*ns and ts are integers. | *ns and ts are integers. | ||
Revision as of 05:58, 11 November 2013
BINOMDIST (ns, ts, ps, cu)
- ns is the number of successes in trials.
- ts is the number of independent trials.
- ps is the probability of success on each trial
- 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:
- A number of tests should be fixed.
- Each test must be independent.
- Each test represents only two results(Success/Failure)
- No test has any impact on any other test.
should be fixed.For example, the number of ways to achieve 2 heads in a set of four tosses is "4 choose 2".
- In BINOMDIST function, NS is the number of successes in trials.
- TS is the number trials to be made, also NS and TS should be integers.
- And PS is number of probability of success on each independent trials.
- Finally 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
- NS and TS are not an Integer.
- NS,TS and PS are not a numeric.
- NS<0 or NS>TS.
- Also PS<0 or PS>1.
The binomial distribution with parameters n and p, we write . The probability of getting exactly successes in trials is given by the Probability Mass Function: ,for k=0,1,2,3...n where (n,k)is the COMBIN(n,k) i.e.
.
The probability of getting exactly 
successes in 
,for k=0,1,2,3...n where (n,k)is the COMBIN(n,k) i.e.
The Cumulative Binomial Ditrbution is: = Failed to parse (unknown function "\x"): {\displaystyle Pr(X<=x) =\sum_{n=0}^\x \binom{n}{i}p^{i}(1-p)^{(n-i)}}
= Failed to parse (unknown function "\x"): {\displaystyle Pr(X<=x) =\sum_{n=0}^\x \binom{n}{i}p^{i}(1-p)^{(n-i)}}
- It calculates the individual term Binomial Distribution Probability.
- ns and ts are integers.
- When ns or ts or ps is non-numeric BINOMDIST displays error.
- When ns is less than 0 or greater than t, BINOMDIST shows NaN.
When ps is less than 0 or greater than 1, BINOMDIST calculates the wrong result. = BINOMDIST (4, 12, 0.3, FALSE) is 0.2311
Example
| Column1 | Column2 | Column3 | Column4 | |
| Row1 | 4 | 12 | 0.3 | FALSE |
| Row2 | 0.2311 | |||
| Row3 | ||||
| Row4 | ||||
| Row5 | ||||
| Row6 |