# BinomialDist Command

##### Command Categories (All commands)

BinomialDist( <Number of Trials>, <Probability of Success> )
Returns a bar graph of a Binomial distribution.
The parameter Number of Trials specifies the number of independent Bernoulli trials and the parameter Probability of Success specifies the probability of success in one trial.
BinomialDist( <Number of Trials>, <Probability of Success>, <Boolean Cumulative> )
Returns a bar graph of a Binomial distribution when Cumulative = false.
Returns a graph of a cumulative Binomial distribution when Cumulative = true.
First two parameters are same as above.
BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
Let X be a Binomial random variable and let v be the variable value.
Returns P( X = v) when Cumulative = false.
Returns P( X ≤ v) when Cumulative = true.
First two parameters are same as above.
Note: A simplified syntax is available to calculate P(u ≤ X ≤ v): e.g. BinomialDist(10, 0.2, 1..3) yields 0.77175, that is the same as BinomialDist(10, 0.2, {1, 2, 3}). This syntax also works in the CAS View

## CAS Specific Syntax

In CAS View only one syntax is allowed:

BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
Let X be a Binomial random variable and let v be the variable value.
Returns P( X = v) when Cumulative = false.
Returns P( X ≤ v) when Cumulative = true.
Example:
Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is \mathrm{\mathsf{ \frac{1}{10} }}, hence the propability of transfering an arbitrary packet successfully is \mathrm{\mathsf{ \frac{9}{10} }}.
• BinomialDist(3, 0.9, 0, false) yields \mathrm{\mathsf{ \frac{1}{1000} }}, the probability of none of the three packets being transferred successfully.
• BinomialDist(3, 0.9, 1, false) yields \mathrm{\mathsf{ \frac{27}{1000} }}, the probability of exactly one of three packets being transferred successfully.
• BinomialDist(3, 0.9, 2, false) yields \mathrm{\mathsf{ \frac{243}{1000} }}, the probability of exactly two of three packets being transferred successfully.
• BinomialDist(3, 0.9, 3, false) yields \mathrm{\mathsf{ \frac{729}{1000} }}, the probability of all three packets being transferred successfully.
• BinomialDist(3, 0.9, 0, true) yields \mathrm{\mathsf{ \frac{1}{1000} }}, the probability of none of the three packets being transferred successfully.
• BinomialDist(3, 0.9, 1, true) yields \mathrm{\mathsf{ \frac{7}{250} }}, the probability of at most one of three packets being transferred successfully.
• BinomialDist(3, 0.9, 2, true) yields \mathrm{\mathsf{ \frac{271}{1000} }}, the probability of at most two of three packets being transferred successfully.
• BinomialDist(3, 0.9, 3, true) yields 1, the probability of at most three of three packets being transferred successfully.
• BinomialDist(3, 0.9, 4, false) yields 0, the probability of exactly four of three packets being transferred successfully.
• BinomialDist(3, 0.9, 4, true) yields 1, the probability of at most four of three packets being transferred successfully.
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