
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 12th, 2012, 05:38 PM  #1 
Member Joined: Apr 2011 Posts: 31 Thanks: 0  Error with Moment Generating Functions
Just a warning, I may use improper terms here. If you think I'm explaining something wrong, it's quite possible that I am. Just let me know. I'm trying to calculate the second moment for a binomial distribution. E(y^2), where Y ~ Binom. I have two different methods, both of which I believe should work, but I'm getting different results. Could someone help me find which one I've done incorrectly? V(Y) = E(y^2)  E(y)^2 ==> npq = E(y^2)  (np)^2 ==> E(y^2) = np(q + np) The second method I'm using is with the second moment of the moment generating function. My thinking is that if I take the MGF for the binomial distribution, take its derivative, and set t = 0, I should get E(y^2) mgf = (p*e^t + q)^n mgf(first derivative) = n*p*e^t*(p*e^t + q)^(n1) mgf(first derivative, t = 0) = n*p*(p + q)^(n1) mgf(first derivative, t = 0) = n*p Obviously these both can't be right. I'm thinking the first one is correct, but where did I mess up? 
February 13th, 2012, 03:18 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,256 Thanks: 508  Re: Error with Moment Generating Functions Quote:
Your second method (moment generator) is correct. However what you got is the first moment (mean), not the second moment. You need to use the second derivative to get the second moment.  
February 13th, 2012, 03:57 PM  #3 
Member Joined: Apr 2011 Posts: 31 Thanks: 0  Re: Error with Moment Generating Functions
Ohhh, my goodness. Of course. Thank you


Tags 
error, functions, generating, moment 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Moment generating function to PMF  FreaKariDunk  Algebra  3  October 19th, 2012 07:01 AM 
Derive the momentgenerating function of Y bar  450081592  Advanced Statistics  1  November 26th, 2011 02:04 PM 
approaching moment generating function standard normal  fc_groningen  Advanced Statistics  0  March 7th, 2011 08:02 AM 
Generating functions  (1xx^2x^3x^4x^5x^6)^1  KristopherWindsor  Advanced Statistics  4  May 3rd, 2010 08:47 AM 
Generating functions  (1xx^2x^3x^4x^5x^6)^1  KristopherWindsor  Number Theory  0  January 1st, 1970 12:00 AM 