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N
XN
GX(z) = X
k≥0
P r(X=k)zk.
z
X zX
GX(z) = X
ω∈Ω
P r(ω)zX(ω).
A={a, b, c, d}L
a,b,c
L={a,b,c}*d
A
1
4d
L
L={w∈A∗|w d
d}
={a, b, c}∗d
Ω = L
∈L
P r(ababad) = 1
4.1 4.1 4.1 4.1 4.1 4=1
46
X L
P r(X=k) = 3k−1
4k
X
GX(z) = ∞
X
k=1
3k−1
4kzk=z 4−3z.
X GX(z)
G(1) = 1.

•EX=G′(1)
•VX=G′′(1) + G′(1) −[G′(1)]2.
L
k1
4k
G(1) = 1.
G
G′(z) = d
dzG(z) = 4 (4 −3z)2
G′′(z) = 4.2.3.(4 −3z)
(4 −3z)4=24 (4 −3z)3.
•EX=G′(1) = 4
•VX=G′′(1) + G′(1) −[G′(1)]2= 24 + 4 −42=12
X Y
X+Y
X Y
GX+Y(z) = GX(z)GY(z).
{a, b, c, d}d

a,b,c d
L2={a,b,c}*d{a,b,c}*d
da,b,c
L2 = LL
w L2u∈L
v∈L
L
|w|=|u|+|v|X=|u|Y=|v|
S=X+Y L2
GS(z) = GX(z)GY(z) = z
4−3z2
=z2
(4 −3z)2.
S GS(z)
•ES= 4 + 4 = 8
•VS= 12 + 12 = 24.
X
p q p, q ∈[0,1] p+q= 1
•EX=p
•VX=pq
•σX =√pq
A
p
P r(A) = EA.
n
p
q= 1 −p X =
X k
[0, n]
pk=P r(X=k) = n
kpkqn−k.
n
k=Ck
n=n!
k!(n−k)!
X n p
X
n
pEX=np VX=npq σX =√npq

p > 0
q= 1 −p
X
k∈N∗
pk=P r(X=k) = qk−1p.
X p
•EX=1
p
•VX=q
p2
•σX =√q
p
X λ X
k∈N
pk=P r(X=k) = λk
k!e−λ.
•EX=λ
•VX=λ
•σX =√λ
λ

λ µ λ +µ
Xnpn
nlimn→∞ npn=λ > 0k∈N
limn→∞P r(Xn=k) = e−λλk
k!.