BinomialDist Command

BinomialDist[ <Number of Trials>, <Probability of Success> ]

Returns a bar graph of a Binomial distribution.

Parameters:

Number of Trials: number of independent Bernoulli trials

Probability of Success: 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 bar 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 v>, <Boolean Cumulative> ]

Let X be a Binomial random variable.

Returns P( X = v) when Cumulative = false.

Returns P( X ≤ v) when Cumulative = true.

First two parameters are same as above.

CAS Specific Syntax

In CAS View only one syntax is allowed:

BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value v>, <Boolean Cumulative> ]

Let X be a Binomial random variable.

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 \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.