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Suppose X is a continuous random variable with pdf given by f(x).
The expected value (or mean) of X denoted by E(X) or mX (or more commonly, just m) is defined as
Similarly, the expected value of some arbitrary function h(X) of the random variable X (note that h(X) is also a r.v.) is defined as
The variance of X denoted by V(X) or s2X (or just s2) is defined as:
As with discrete r.v.’s, we may use the shortcut for s2:
The standard deviation (SD) of X, denoted by
s
is equal to Ös2
NOTE: As with discrete r.v.’s we have E[aX+b]=aE[X]+b and V[aX+b] = a2V(X)
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Next: Uniform Distribution
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