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Grinstead-Snell-Probability
· Problem 6.3.19
Sums of Random Variables
Mathematics · correlation
Problem
Let
X
X
X
and
Y
Y
Y
be independent random variables with uniform densities in
[
0
,
1
]
[0, 1]
[
0
,
1
]
. Let
Z
=
X
+
Y
Z = X + Y
Z
=
X
+
Y
and
W
=
X
−
Y
W = X - Y
W
=
X
−
Y
. Find (a)
ρ
(
X
,
Y
)
\rho(X, Y)
ρ
(
X
,
Y
)
(see Exercise 18). (b)
ρ
(
X
,
Z
)
\rho(X, Z)
ρ
(
X
,
Z
)
. (c)
ρ
(
Y
,
W
)
\rho(Y, W)
ρ
(
Y
,
W
)
. (d)
ρ
(
Z
,
W
)
\rho(Z, W)
ρ
(
Z
,
W
)
.
Related theory
Correlation And The Correlation Coefficient
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