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Miklós Schweitzer
1968 Miklós Schweitzer
11
Miklos Schweitzer 1968_11
Miklos Schweitzer 1968_11
Source:
October 8, 2008
probability
probability and stats
Problem Statement
Let
A
1
,
.
.
.
,
A
n
A_1,...,A_n
A
1
,
...
,
A
n
be arbitrary events in a probability field. Denote by
C
k
C_k
C
k
the event that at least
k
k
k
of
A
1
,
.
.
.
,
A
n
A_1,...,A_n
A
1
,
...
,
A
n
occur. Prove that
∏
k
=
1
n
P
(
C
k
)
≤
∏
k
=
1
n
P
(
A
k
)
.
\prod_{k=1}^n P(C_k) \leq \prod_{k=1}^n P(A_k).
k
=
1
∏
n
P
(
C
k
)
≤
k
=
1
∏
n
P
(
A
k
)
.
A. Renyi
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