Going over my Lecture Notes my Lecturer as Started with(adsbygoogle = window.adsbygoogle || []).push({});

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.

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

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