Math
1271:
Section
6.8
Probability
Page
5
of
7
Math12T]
Lectwre
14
5.
Median
Another
measure
of
a
probability
density
function
is
the
me
dian.
Tfiefinitiorg
The
median
m
of
a
probability
density
function,
is
a
number,
defined
as
1
o
1
.
/f'i
f(z)dz
=
5
and
/@
flz)dz
=
5.
Actually,
median
is
a
value
separating
the
higher
half
from
the
lower
half.
Example
3:
Find
the
median
of
the
exponential
distribution
with
mean
p
=
10.
:
"sdth,
e
f('l'):
io
t<o

t
"}'{8
"
t2o

(0
t<co
{_l_lo_e'lo
{';0
m
=
=)
fwde
AN
frrdt
=0
%
&

00
s
(=0°,
m)
f(f):o
Thew
m
>0
g
:
¢

4
:'f
('f,df
!f
H.)d{
i
te
[
fwd
e
[y

t
o
s
y
lm
~
1o

to
7
o
=€
=
(~1)
{0
—'%:u[—
.
=
[e®
e
lo'

_2'_.
w
=
Il
m
o
ed
h(e®)
=
In(%
)
=
Ine)
=
In(z)
2073'"(2)
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