This preview shows pages 1–2. Sign up to view the full content.
April 12
HWK #9 due R(4/19) or F(4/20)
11.2: 8, 24, 27, 33
9.2: 4, 12, 16, 22, 27, 34, 40
Prelim 3 Tuesday April 24
7:309 in Uris Hall Auditorium
Covers up to and including 9.2
Definitions
22
probability density
expected
A
value
mea
()
h
a
s
() 0
and
( )
1
The
or
The
(
)
( )
n
va
(
riance
)
fx
fxd
x
EX
xf x dx
xf
x
d
x
xfxd
x
µ
σµ
≥
=
==
=−
∫
∫
∫
∫
Uniform distribution with b=0
2
0
23
2
2
0
22 2
2
1
( )
for
[0, ]
midpoint
33
341
2
b
b
a
b
b
a
x
b
b
xxb
EX
dx
bb
xx
b
EX
dx
bbb
EX
=∈
=
=
=
−=−=
∫
∫
Uniform distribution
formulas for the general case
2
2
2
1
f
o
r
[,]
2(
)
midpoint
2(
)
2
depends only on length
12
b
b
a
a
x ab
ba
EX
dx
ba ba
σ
−
−−
−+
−
−
=
∫
Interpretations
2
The mean
is the average value of
The variance
= (
)
( )
measures how spread out the distribution is.
The
has the right units. For unifor
st
m
(
) /12
(
) / 12
andard deviation
X
x
d
x
σσ
−
=
∫
Exponential
0
2
2
2
0
00
2
exponential
( )
mean
1/
, '
() 2, ()
20
21 1
1
variance
rt
rt
rt
rt
rt
rt
rt
fx r
e
r
EX
t re
dt
ft t gt r
e
ft
tgt
e
te
te d
t
t
re d
t
rr
rrr
r
−
∞
−
∞∞
∞
−
=
−
+
= +
=
=−=
=
∫
∫∫
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentWhy 1/r?
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '07
 DURRETT
 Calculus, Probability

Click to edit the document details