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For a continuous random variable
defined with a density f,
and expectation ,
its variance is:
Proposition 1:
Var(X+b)=Var(X)
Proposition 2:
Var(aX)=a^{2} Var(X)
Proposition 3:
Only for independent random variables do we have
Examples:
 1.
 For the exponential random variable with parameter ,
I showed:
 2.
 For U a random uniform on [0,1],
I showed:
.
 3.

For the Normal
random variable X:
This is the meaning of the second
parameter in the definiton of the density,
its square root is called the standard deviation
and gives the width
of the curve.
I explained in class what standardizing a variable meant in general,
not just for Normals.
Susan Holmes
19981207