Теория вероятностей. Барышева В.К - 127 стр.

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M[X|Y = 2]
P (X = −1|Y = 2) =
P (X = −1, Y = 2)
P (Y = 2)
=
=
1/12
1/3
=
1
4
P (X = 0|Y = 2) =
P (X = 0, Y = 2)
P (Y = 2)
=
=
1/6
1/3
=
1
2
P (X = 1|Y = 2) =
P (X = 1, Y = 2)
P (Y = 2)
=
1/12
1/3
=
1
4
X Y = 0
X −1 0 1
P (X|Y = 0) 1/6 4/6 1/6
X Y = 2
X −1 0 1
P (X|Y = 2) 1/4 1/2 1/4
M[X|Y = 0] = −1 ·
1
8
+ 0 ·
3
4
+ 1 ·
1
8
= 0,
M[X|Y = 2] = −1 ·
1
4
+ 0 ·
1
2
+ 1 ·
1
4
= 0.
m
x
= −1 ·
1
6
+ 0 ·
4
6
+ 1 ·
1
6
= 0;
m
y
= 0 ·
2
3
+ 2 ·
1
3
=
2
3
.
cov (X, Y ) = M[XY ] − m
x
m
y
=
=
−1 · 0 ·
1
12
+ 0 · 0 ·
1
2
+ 1 · 0 ·
1
12
− 1 · 2 ·
1
12
+ 0 · 2 ·
1
6
+
+1 · 2 ·
1
12
− 0 ·
2
3
= 0,
X Y
X Y
P (X = −1, Y = 0) =
1
12
,

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