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Show that a Gaussian Distribution Corresponds to a CTS random variable.

  1. Dec 13, 2011 #1
    Going over my Lecture Notes my Lecturer as Started with

    Show that a Gaussian Distribution Corresponds to a CTS random variable.

    Then she has

    i) Taken the f(x) = [p.d.f] and shown a) f(x) >= 0 for all x member of real numbers. b) Integral over all real numbers = 1

    ii) Found the M.G.F then taken the first two derivatives of MGF and calculated variance.

    iii) Taken two independent Gaussians and taken a linear combination i.e. aX+bY and found a new mean and variance.

    My Problems are.
    1) How does this shove the initial problem? (this is my only stats module and is this ticking off a definition?)
    2) Why Calculate the Variance from the M.G.F
    3) What does finding the new mean and variance achieve in case iii)

    This is a bit of a complicated question any help would be really appreciated.

    Thanks.
     
  2. jcsd
  3. Dec 13, 2011 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    You should clarify your question somewhat. Start by defining CTS. Statement i) is very confusing.
     
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