A First Course in Quality Engineering, 2nd Edition

94 A First Course in Quality Engineering

µ

X

x

xp x=

( )

∑

If X is a continuous random variable with pdf f(x), then the mean is

dened as:

µ

X

x

xf x dx=

( )

∫

2� Variance:

If X is a discrete random variable with pmf p(x), then the variance is

dened as:

σ µ

X X

x

x p x

2

2

= −

( )

( )

∑

If X is a continuous random variable with pdf f(x), then the variance

is dened as:

σ µ

X X

x

x f x dx

2

2

= −

( )

( )

∫

From the denition of the mean μ

X

, we can see that the mean is a weighted

average, which represents the center of gravity of a distribution and indi-

cates where a distribution is located on the x-axis� The variance σ 

2

X

is the

weighted average of the squared deviations of the values of the variable

from its mean� It says how dispersed the distributi ...