# Cumulative distribution functions: cdf

### 8.4.20 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