TD 3 - Ceremade

Xn
p Yn:= XnXn+1
Un=Y1+. . . +Yn
Yn
Yi
Un
5%
[|0, n|]
X1X2
p T =max(X1, X2)
Z=min(X1, X2)q= 1 −p
X1+X2X1−X2
X1+X2|X1−X2|T Z
P(X1=X2) = p
1+q
Z1−q2
Z
{Z=k}∩{T=k}={X1=k}∩{X2=k}
T
X p (0 <p<1)
P(X=k) = p(1 −p)k−1k > 0
∀(k, n)∈N∗2, P (X > n +k|X > k) = P(X > n).
P(λ)
p
Z
Z

A B
X
P(λ)A i−
B(p)Yip i−
A0 1 −p
(X, Yi)
S=
X
X
k=1
Yk
S
P(S=k|X=n)
S
P(X=n|S=k)
l
p
[0, l]x≤l
P(C) = p P (A) + P(B) = p
104
53 130 63
X Y
fXfYU=min(X, Y )V=max(X, Y )
U V fUfV
Xn
λ1, . . . , λnMin(X1, X2,...Xn)
n
i
λiY
Y
A[0, x]B x C
N(0,1)
73