563489578934

TABLE B–1
SOME DISTRIBUTIONS AND THEIR PROPERTIES
Equation for:
696
Name of
Distribution Type Sketch of PDF
Cumulative Distribution
Function (CDF)
Probability Density
Function (PDF)
Mean Variance
Binomial
Discrete
f (x)
0.5
n = 3
p = 0.6
0 1 2 3 4 5
x
F(a) = g m
P(k)
k = 0
m … a
where
P(k) = a n k bpk (1 - p) n-k
f(x) = g n
k = 0
P(k)d(x - k) np np (1 - p)
where
P(k) = a n k bpk (1 - p) n-k
Poisson
Discrete
f (x)
0.3
l = 2
0 1 2 3 4 5 6
x
F(a) = g m
P(k)
k = 0
m … a
where
f(x) = g q
P(k)d(xk) l l
k = 0
where
P(k) = lk
k! e-l P(k) = lk
k! e-l
Uniform
Continuous
f (x)
1
A
m – –– 2
A
A
m m + ––
A
2
x
1
F(a) = f
A
0, a 6 ¢ 2m - A ≤
2
2m - A
Ba - ¢ ≤R , ƒ a - m ƒ … A 2
2
1, a Ú ¢ 2m - A ≤
2
0, x 6 ¢ 2m - A ≤
2
1
f(x) = f
A , |x - m| … A 2
0, x 7 ¢ 2m + A ≤
2
m
A 2
12
Gaussian
Continuous
f (x)
m
s
x
1
2pa
F(a) = Qa m - a
s b f(x) = 1
12ps exp [-(x - m)2 >2s 2 ] m s 2
where
Q(s) ! 1 q
e -x2 >2 dx
12p La
Sinusoidal
Continuous
1
pA
– A
A
x
0, a … -A
1
F(a) = e
p Bp 2 + sin-1 ¢ a A ≤R, |a| … A
1, a Ú A
0, x 6-A
1
f(x) = e
p2A 2 - x 2, |x| … A
0, x 7 A
0
A 2
2