BinomialDist Command

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.

BinomialDist( <Number of Trials>, <Probability of Success>, <List of values>)

Calculates P(u ≤ X ≤ v) by applying the previous syntax (with Cumulative = false) and adding the values obtained when the elements of the List of values are used as variable values.

BinomialDist(10, 0.2, {1,2,3}) yields 0.77175, and is equivalent to BinomialDist(10, 0.2, 1, false) + BinomialDist(10, 0.2, 2, false) + BinomialDist(10, 0.2, 3, false)

The syntaxes BinomialDist(10, 0.2, {1,2,3}) and BinomialDist(10, 0.2, 1..3) are equivalent.

CAS Syntax

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.

You can plot a graph with eg f(x):=BinomialDist(100,x,36,true)-BinomialDist(100,x,23,true)

Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is \(\frac{1}{10}\), hence the propability of transfering an arbitrary packet successfully is \(\frac{9}{10}\).

  • BinomialDist(3, 0.9, 0, false) yields \(\frac{1}{1000}\), the probability of none of the three packets being transferred successfully.

  • BinomialDist(3, 0.9, 1, false) yields \(\frac{27}{1000}\), the probability of exactly one of three packets being transferred successfully.

  • BinomialDist(3, 0.9, 2, false) yields \(\frac{243}{1000}\), the probability of exactly two of three packets being transferred successfully.

  • BinomialDist(3, 0.9, 3, false) yields \(\frac{729}{1000}\), the probability of all three packets being transferred successfully.

  • BinomialDist(3, 0.9, 0, true) yields \(\frac{1}{1000}\), the probability of none of the three packets being transferred successfully.

  • BinomialDist(3, 0.9, 1, true) yields \(\frac{7}{250}\), the probability of at most one of three packets being transferred successfully.

  • BinomialDist(3, 0.9, 2, true) yields \(\frac{271}{1000}\), 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.

BinomialDist( <Number of Trials>, <Probability of Success>, <List of values>)

Calculates P(u ≤ X ≤ v) by applying the previous syntax (with Cumulative = false) and adding the values obtained when the elements of the List of values are used as variable values.

BinomialDist(10, 0.2, {1,2,3}) yields \(\frac{1507328}{1953125}\), and is equivalent to BinomialDist(10, 0.2, 1, false) + BinomialDist(10, 0.2, 2, false) + BinomialDist(10, 0.2, 3, false)