# Moment generating functions

• Jan 20th 2009, 09:38 AM
MS330
Moment generating functions
Hey guys,

Any idea how to find the moment generating function? I know for discrete ones it's the SUM{e^(tx)p(x)}, but I don't understand how to actually go about doing that.

Any ideas?
• Jan 20th 2009, 12:26 PM
Last_Singularity
Quote:

Originally Posted by MS330
Hey guys,

Any idea how to find the moment generating function? I know for discrete ones it's the SUM{e^(tx)p(x)}, but I don't understand how to actually go about doing that.

Any ideas?

Example: let \$\displaystyle x\$ be a discrete random variable. And suppose that it takes that values \$\displaystyle x=1\$ with probability 0.2, \$\displaystyle x=2\$ with probability 0.3, and \$\displaystyle x=3\$ with probability 0.5.

Then its moment generating function is:
\$\displaystyle e^t (0.2) + e^{2t} (0.3) + e^{3t} (0.5)\$
• Jan 20th 2009, 12:28 PM
MS330
How would I do it if I was asked to find the mgf for the possion distribution, with no values given?
• Jan 20th 2009, 03:21 PM
Last_Singularity
Quote:

Originally Posted by MS330
How would I do it if I was asked to find the mgf for the possion distribution, with no values given?