9.4.20  Cumulative distribution functions: cdf

The cdf command finds the cumulative distribution function for a probability distribution.

• cdf takes one or more mandatory arguments and one optional argument.
  • distd, the name of the function that finds the distribution’s density function.
  • parameters, any parameters that would normally be passed to distd.
  • x, a number.
• cdf(distd,parameters) returns an expression for the cumulative distribution function for distd with parameters parameters.
• cdf(distd,parameters,x) returns the value of the cumulative distribution function at x. parameters.

Examples.

• Input:
  cdf(normald,0,1)
  Output:

  erf ⎛ ⎜ ⎜ ⎝ 1 2  x  √ 2 ⎞ ⎟ ⎟ ⎠ +1 2

• Input:
  cdf(binomial,10,0.5,4)
  Output:

  0.376953125