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Proposition 1:

Proposition 2:

If *X* is a continuous random variable
with probability density function
*f*(*x*) then for any real valued
function *g*:

Proposition 3:

*E*(*aX*+*b*)=*aE*(*X*)+*b*

Proposition 4:

Only for independent random variables do we have

Examples:

For the exponential random variable with parameter ,
I showed:

For *U* a random uniform on [0,1],
I showed:
.

*Susan Holmes*

*1998-12-07*