### 20.4.19 Moment generating functions for probability distributions

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.
  - params, any parameters that would normally be passed to distd.
- mgf(distd,params) returns an expression for the moment generating function for distd with parameters params.

#### Examples

Find the moment generating function for the standard normal distribution:

mgf(normald,1,0)

et |  |  |  |  |  |  |  |  |  |

Find the moment generating function for the binomial distribution:

mgf(binomial,n,p)

| ⎛ ⎝ | 1−p+p et | ⎞ ⎠ | n