My Math Forum Moment generating function
 User Name Remember Me? Password

 Advanced Statistics Advanced Probability and Statistics Math Forum

 May 7th, 2016, 08:15 AM #1 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Moment generating function If I have a sequence of independent random variables having a standard normal distribution. Suppose N has a poisson distribution with mean $\displaystyle \lambda$ and is independent of this sequence. Define a new random variable W = sum of Xi from i=0 to N. Show moment generating function of W is: $\displaystyle Mw(\phi) = e^{\lambda(e^{0.5\phi^2 -1)}}$ I thought to get this I would just take the moment generating function of a poission i.e $\displaystyle e^{\lambda(e^{\phi}-1})$ to the power of N, but its not the answer?
 May 22nd, 2016, 01:52 AM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Hey calypso. I'd take a look at the MGF identity for adding two Normal distributions conditional on the value of N. Once you get the probability density function you can take the MGF of that. It means you have to figure out a conditional probability given the value of N (so you look at the probability of getting a particular value of N) and then use that value to determine your MGF. If you are looking at overall expectations then you can use the total expectation laws which look at finding expectations of conditional random variables. Please post your attempts so we can have a look at them and give further guidance.

 Tags function, generating, moment

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post calypso Advanced Statistics 0 November 15th, 2015 11:35 AM theorem Advanced Statistics 3 May 3rd, 2014 12:54 PM FreaKariDunk Algebra 3 October 19th, 2012 07:01 AM 450081592 Advanced Statistics 1 November 26th, 2011 01:04 PM fc_groningen Advanced Statistics 0 March 7th, 2011 07:02 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top