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Putnam
1968 Putnam
B1
B1
Part of
1968 Putnam
Problems
(1)
Putnam 1968 B1
Source: Putnam 1968
2/19/2022
The random variables
X
,
Y
X, Y
X
,
Y
can each take a finite number of integer values. They are not necessarily independent. Express
P
(
min
(
X
,
Y
)
=
k
)
P(\min(X,Y)=k)
P
(
min
(
X
,
Y
)
=
k
)
in terms of
p
1
=
P
(
X
=
k
)
p_1=P(X=k)
p
1
=
P
(
X
=
k
)
,
p
2
=
P
(
Y
=
k
)
p_2=P(Y=k)
p
2
=
P
(
Y
=
k
)
and
p
3
=
P
(
max
(
X
,
Y
)
=
k
)
p_3=P(\max(X,Y)=k)
p
3
=
P
(
max
(
X
,
Y
)
=
k
)
.
Putnam
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