Corrige.

N
M
n∈Nm > 0
P(N=n, M > m) = e−αm n
n!e−exp(−αm)(θ−m)c θc[0,θ](m)
α∈Rθ > 0c > 0
[0,θ](m)=1 m∈[0, θ] 0
P(M > m)m > 0M
α θ c
P(M > m) = Pn∈NP(n=n, M > m) = (θ−m)c
θc[0,θ](m)
fM(m)P(M6m)fM(m) = c(θ−m)c−1
θc[0,θ](m)
N|M > m λm
N M
P(N|M > m) = P(N=n,M>m)
P(M>m)
λm=e−αm
λm= exp(a−αm)
N M N |M > m m
N(m)=(N|M > m)
m m > 0N(m)
λm
P(N(m) = n) = λn
m
n!e−λm.
m
λm
EN(m) = λm

365/EN(m) = 365/λm
P(N(m)>1) = 1 −
P(N= 0) = 1 −e−λm
N1(m), N2(m),...Nk(m)
k(Ni(m))i=1,...,p
Xk=1
kPk
i=1 Ni(m)λmk
Ni(m)ENi(m) = λm
Xk
Ni(m)ENi(m) = λmV ar(Ni(m)) = λm
√kXk−λm
√λm
loi
→ N(0,1)
XkN(λm,λm
k)k
λm= 0.1
k= 10
P(X10 >0.3)
P(X10 >0.3) 'P(U>2) U∼ N(0,1)
P(X10 >0.3) '1−0.9772 = 0.0228
2.3%
N{1, . . . , N}Xkk
Kii
pi,j =(1/Kii j
0i j.

P(Xk+1 =j|Xk=
i) = pi,j k∈Nj
G
G=
? 1/3 1/3 1/3 0
? 0 1/2 0 1/2
? 1 0 0 0
? 1/4 1/4 0 1/4
? 0 1/3 1/3 0
N p2,3
N= 5 p2,3= 1/2
3
π(1) =0.2 0.2 0.2 0.2 0.2
π(2) =0.09 0.34 0.29 0.09 0.19
π(3) =0.15 0.64 0.27 0.54 0.19
π(4) =−0.09 0.48 0.29 0.54 −0.14
π(2) π(3) π(4)
π(1)
2
Xk
k p = 0.4
1−p k ∈N P(Xk= 1) = p
Xk
90% 10%
Ykk

Yk= 1
P(Yk= 1) = P(Yk= 1|Xk= 1)P(Xk= 1) + P(Yk= 1|Xk= 0)P(Xk= 0) =
0.9p+ 0.1(1 −p)=0.42
Xk= 1 Yk= 1
P(Xk= 1|Yk= 1) = P(Yk=1|Xk=1)P(Xk=1)
P(Yk=1) '0.86
1
111
3P(Yk= 1|Xk= 1)P(Yk= 0|Xk= 1)2= 2.7%