Page 50 - Probability, Random Variables and Random Processes

RANDOM VARIABLES [CHAP 2

Properties of fx(x) :

3. fx(x) is piecewise continuous.

The cdf FX(x) of a continuous r.v. X can be obtained by

By Eq. (2.19), if X is a continuous r.v., then

2.6 MEAN AND VARIANCE

A. Mean:
The mean (or expected ualue) of a rev. X, denoted by px or E(X), is defined by

X: discrete
px = E(X) =
xfx(x) dx X: continuous

B. Moment:
= irx(xk)
The nth moment of a r.v. X is defined by

E(.n) X: discrete
xnfdx) dx X: continuous

Note that the mean of X is the first moment of X.

C. Variance:
The variance of a r.v. X, denoted by ax2 or Var(X), is defined by
ox2 = Var(X) = E{[X - E(X)I2}
Thus,

rC (xk - pX)2pX(~J X : discrete

eX2 = 1 im px)2/x(x) dx x: continuous
-
(X