Pascal Command

Pascal( <n>, <p> )

Returns a bar graph of a Pascal distribution.

The Pascal distribution models the number of failures before the nth success in repeated mutually independent Bernoulli trials, each with probability of success p.

Pascal( <n>, <p>, <Boolean Cumulative> )

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

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

First two parameters are same as above.

Pascal( <n>, <p>, <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.

Note: This command also works in the CAS View.

Example:

If 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}, then the probability of 2 failures before the success is given by

Pascal(1, 1/6, 2, false) which yields 0.12 in the Algebra View and 25/216 in the CAS View.