I+.05 method:
(  . ) *
=
i 0 5 n 100
k
for kth %ile. Returns item place in array of
ordered set. K as integer.
N+1 method:
+ =
kn 1
i
. K in decimal form.
For interpolators (e.g. 3.5), ipart +
fpart(largersmaller).
Sample mean is just average
Sample variance
= =
(
 )

s2
i
1n xi x 2n 1
PDFs (Probability Distribution Functions):
P(a<x<b) =
abfxdx
1)
F(x) >= 0 i.e.
=
fx
kx2
< < ,
for 0 x 2
0
elsewhere
2)
∞∞ ( )
f x
=
1
3)
CDF (Cumulative Distribution Functions):
4)
F(x) = P(X<x) =
∞
xfudu
. Shows amount of
probability to that point.
5)
f(x) = some PDF
6)
µ=E[x]=
∞∞
xfxdx
7)
=
=∞∞(

)
= ∞∞

σ2
Vx
x μ 2fxdx
x2fxdx μ2
8)
Normal Distribution:
9)
X:n(µ, σ
2
) >
= 
Z
x μσ
10)
P(Z>z)=P(Z<z)
11)
12)
PMFs (Probability Mass Functions):
1)
F(x) >= 0 for all x
2)
( )
f x
=1
3)
=
=
( )
μ
Ex
xf x
4)
=
=

σ2
VX
Ex2 μ2
5)
=
≤ =∞
→
=
< ,
=
F
PX
x
xfx
Fx
0 for x 1
Fx
18 for
≤ ≤ ,
.
1
x
3
etc
6)
Binomial distribution (discrete):
7)
Deals with some # of trials with one of two outcomes
(success or failure in general)
8)
:
, →
= (
)
(  )  , = , , ,
X bn p
fx
xn px 1 p n x
x
0 1 2
…
n
9)
E[x]=np
10)
V(x)=np(1p)
11)
CDF of:
0xpdf
12)
Poisson Distribution (discrete):
13)
P(X=x)=

!
e λλxx
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 Spring '06
 andersonrowland
 Normal Distribution, Probability theory, Cumulative distribution function, probability distribution functions, Poisson Joint PDFs, Poisson process PDF

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