Manuals/calci/BINOMDIST

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:

1. A number of tests $n$ 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, 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

1. NS and TS are not an Integer.
2. NS,TS and PS are not a numeric.
3. NS<0 or NS>TS.
4. Also PS<0 or PS>1.

The binomial distribution with parameters n and p, we write $X{\tilde {}}B(n,p)$. The probability of getting exactly $k$ successes in $n$ trials is given by the Probability Mass Function: $b(k;n,p)=Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}$,for k=0,1,2,3...n where (n,k)is the COMBIN(n,k) i.e.$(n,k)={\frac {n!}{k!(n-k)}}!$

The Cumulative Binomial Ditrbution is:$B(x;n,p)$ = 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 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