Pascal Command

Pascal[ <Number of Successes>, <Probability of Success> ]

Returns a bar graph of a Pascal distribution.

Parameters:

Number of Successes: number of independent Bernoulli trials that must be successful

Probability of Success: probability of success in one trial

Pascal[ <Number of Successes>, <Probability of Success>, <Boolean Cumulative> ]

Returns a bar graph of a Pascal distribution when Cumulative = false. Returns a bar graph of a cumulative Pascal distribution when Cumulative = true.

First two parameters are same as above.

Pascal[ <Number of Successes>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ]

Let X be a Pascal random variable and v the variable value.

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

First two parameters are same as above.

CAS Syntax

Pascal[ <Number of Successes>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ]

Let X be a Pascal random variable.

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

Example:

The number of independent Bernoulli trials that must be successful is n = 1, the probability of success in one trial is p = \frac{1}{6}, the variable value is v = 2 and "Cumulative" = false.

Pascal[ n, p, v, false] yields \frac{25}{216}