Combining Random Variables
AP Statistics · Flashcards · Application
AP STATISTICS · FLASHCARDS
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QUESTION
What is the variance of
X
+
Y
+
Z
X + Y + Z
X
+
Y
+
Z
given
Var
(
X
)
=
1
\text{Var}(X) = 1
Var
(
X
)
=
1
,
Var
(
Y
)
=
2
\text{Var}(Y) = 2
Var
(
Y
)
=
2
,
Var
(
Z
)
=
3
\text{Var}(Z) = 3
Var
(
Z
)
=
3
, assuming independence?
QUESTION
What is the mean of
2
X
+
3
Y
2X + 3Y
2
X
+
3
Y
given
E
(
X
)
=
4
\text{E}(X) = 4
E
(
X
)
=
4
and
E
(
Y
)
=
6
\text{E}(Y) = 6
E
(
Y
)
=
6
?
QUESTION
What is the variance of
2
Y
2Y
2
Y
given
Var
(
Y
)
=
4
\text{Var}(Y) = 4
Var
(
Y
)
=
4
?
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ANSWER
Var
(
2
Y
)
=
16
\text{Var}(2Y) = 16
Var
(
2
Y
)
=
16
. Apply variance scaling:
2
2
(
4
)
=
4
(
4
)
=
16
2^2(4) = 4(4) = 16
2
2
(
4
)
=
4
(
4
)
=
16
.
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