exos varalea

1 6
3 3 2 1
1X
1 2
3
X11
X21
X33
X4
X5
5
0.7
k
98%
10 5
R
V R V
6X
X P (X6k)

n1n
7 4
2 5 X
X
X n = 3
n= 5
E(X)n+∞
N
p
n
X X
Y
N n p Y
N= 1000 n= 10 p= 0.01
0; 1; . . . ;k
0Xnn Yn
n
Yn
Xn
n N 1N
N>21
NN
Tn
n
n N Tn
T1T2
n>2P(Tn= 1) P(Tn= 2) P(Tn=n)
n6N n > N
16k6n P (Tn+1 =k) =
k
NP(Tn=k) + N−k+ 1 NP(Tn=k−1)
Gn(x) =
k=n
X
k=1
P(Tn=k)xk

Gn(1)
E(Tn)G0
n(1)
4Gn+1(x) = 1
N(x−
x2)G0
n(x) + xGn(x)
E(Tn+1) = 1−1
NE(Tn)+1
E(Tn)n+∞
n n
p q = 1 −p
X X
n−X
Y
Z=X+Y Z
P(Z= 0) P(Z= 1) npq2n−2(1 +
q)
P(Z=l) =
l
X
k=0
P((X=k)∩(Y=l−k)
PX=k(Y=h)k h
P(Z=l)
n
kn−k l−k=n ll kP(Z=l) = n lpl(1 + q)l(q2)n−l
p(1 + q)=1−q2Z
n2 2 0
2kk k 1n
(1 −q)
n
X
k=1
kqk−1
n
X
k=1
k2k
n>1
n
X
k=1
k22k= (n2−2n+ 3)2n+1 −6
X
X X = 0
X
Y X = 0 Y= 0
k k X Y

k i n p(Y=i/X =k)
Y
n−1
X
i=0
p(Y=i) = 1
Y
c c
n
n > 2
c= 0
X
n Y
Y= 0
X E(X)V(X)
Y P (Y= 0)
k=n
X
k=0
P(Y=k)=1
x6= 1 n>1
k=n
X
k=1
kxk=nxn+2 −(n+ 1)xn+1 +x
(1 −x)2
E(Y)
c6= 0
(Xi)16i6n
i p 2n ZpZp=
i=p
X
i=1
Xi
Zp
X1
PX1=0(X2= 0) PX1=0(X2= 1) PX1=1(X2= 0)
PX1=1(X2= 1) X2
Z2
Zp
p6n−1
PZp=k(Xp+1 = 1)
P(Xp+1 = 1) = 1 + cE(Zp)
2 + pc
Xp
1
2

2n1 2n
X
X
Y U
D
i62n P (U6i)P(D6i)P(Y6i)
P(Y=i) = 2i−1
4n2
Y
n
Z
P(Z=i)i6n
P(Z=i)i>n
2n
X
i=1
P(Z=i)=1
Z X
Y
N b N −b b >1
X
X b = 1
X N = 4 b= 2
X
b−1k
P(X=k) = k−1
b−1
N
b
N b X