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Moment-Generating functions

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Given moment-generation function Msubx(t) = e^(3t+8t^2) find the moment-generating function of the random variable Z = 1/4(X-3) and use it to determine the mean and the variance of Z



    2. Relevant equations



    3. The attempt at a solution

    Honetly I have no idea where to begin. This is the only question I can find of this format in my book that is worded like this, and the examples in my stats book leading up to this just don't cover a question like this, it's all theorems and more basic questions. I messed up my tailbone VERY badly last week and had to miss 2 of my stats lectures which has put me in this position.

    Can someone just help get me started on this and know what I need to do?

    The only thing I can think of is that I have to multiply the Msubx(t) function by e^(tx) and somehow relate it to the r.v. Z?

    I am so confused...not asking for someone to do this for me but could you at least get me started??

    Thanks so much.
     
  2. jcsd
  3. Feb 9, 2010 #2
    Msubx(t) = e^(3t+8t^2) is the moment generation function for a normal distribution.

    The moment-generating function of N(mean,sigma_squared) is
    Msubx(t)= e^(mean*t+.5*sigma_squared*t^2),

    so in this case the mean is 3 and sigma_squared = 16,
    Now try finding the mu and sigma for Z based on the stats for X and then you can use them to write out the moment generation function.

    Is Z=1/(4*(X-3)) or Z=.25*(X-3)? just curious.
     
    Last edited: Feb 9, 2010
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