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.

Find the moment generating function for the standard normal distribution:

mgf(normald,1,0)

e^t

Find the moment generating function for the binomial distribution:

mgf(binomial,n,p)

⎛
⎝

1−p+p e^t

⎞
⎠

ⁿ