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

[andyb177]

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.

 

[mathman]

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