A

A
p
Ap p
A
X
µ V ǫ > 0
P r(|X−µ| ≥ ǫ)≤V
ǫ2.
Xnp=1
10 n∈N
•n= 100 Xn
n
1
10 0.9
•n
≥0.99
•Xn
nn= 100
npq ×1
n2=9 10000.
P r |X100
100 −1 10 |≥ 0.1≤9 10000 ×100 = 0.09 <0.1.
•
P r |Xn
n−1 10| ≥ 0.05≤9 100 ×1 n×1 0.052.
n9
100 ×1 n×1 0.0025 ≤0.01
n≥3600
X
µ V X1, X2, ..., Xn
X
Sn
Sn=1
n
n
X
i=1
Xi.
Snµ
ǫ > 0
lim
n→∞ P r(|Sn−µ|≥ ǫ) = 0.
n
49
4
49
4

m U
U
h
[1, m]
h:U→[1, m].
h U
[1, m]
∀x∈U∀i∈[1, m]P r(h(x) = i) = 1
m.
h
h
x∈U
y∈U v h(x)=h(y)=v
En
P=1
mn.m(m−1)...(m−n+ 1).
m n
n
23
m=365 P
P=1
365n.365.364.363...(365 −n+ 1).
1−P n
n≥23

v[1, m]
nα=n
m
Xm,n
x h(x) = v
m, n → ∞ Xm,n
α
P r(Xm,n =k) = e−ααk
k!,∀k∈N.
v e−α
x
α=n/m
•x
h(x)
•x
Lii
x
h(x)
i∈[1, m]1
m

x
Lii=h(x)
CompRech−(m, n) = 1
m
m
X
i=1
E(Li).
α=n
m
n1
m
Li
CompRech−(m, n) = 1
m×m×n m=n m=α,
x
n1
n
x1, ..., xn
x=x1
x=xi
xi
i−1
CompRech+(m, n) = 1
n
n−1
X
i=0 hCompRech−(m, i) + 1i
= 1 + n(n−1)
2nm
=α
2−1 2m+ 1,
α/2