9.4.19  Moment generating functions for probability distributions: mgf

The mgf command finds the moment generating function for a probability distribution (such as normal, binomial, poisson, beta, gamma).

• mgf takes one or more mandatory arguments:
  • distd, the name of the function that finds the distribution’s density function.
  • parameters, any parameters that would normally be passed to distd.
• mgf(distd,parameters) returns an expression for the moment generating function for distd with parameters parameters.

Examples.

• Find the moment generating function for the standard normal distribution.
  Input:
  mgf(normald,1,0)
  Output:

  et

• Input:
  mgf(binomial,n,p)
  Output:

  ⎛ ⎝

  1−p+p et

  ⎞ ⎠

  n