Теория вероятностей. Барышева В.К - 102 стр.

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0, 27 + 0, 43 + 0, 30 = 1, 0, 55 + 0, 45 = 1.
P (X = 3, Y = −1) = 0, 05 6= 0, 30 ·0, 55 X Y
X Y = 1 :
P (X|Y = 1) =
P (X = x
i
, Y = 1)
P (Y = 1)
⇒ P (X = 1|Y = 1) =
=
P (X = 1, Y = 1)
P (Y = 1)
=
0, 10
0, 45
=
2
9
P (X = 2|Y = 1) =
P (X = 2, Y = 1)
P (Y = 1)
=
0, 30
0, 45
=
6
9
P (X = 3|Y = 1) =
P (X = 3, Y = 1)
P (Y = 1)
=
0, 05
0, 45
=
1
9
P (Y = −1|X = 2) =
P (Y = −1, X = 2)
P (X = 2)
=
0, 13
0, 43
=
13
43
,
P (Y = 1|X = 2) =
P (Y = 1, X = 2)
P (X = 2)
=
0, 30
0, 43
=
30
43
.
{X |Y = 1} 1 2 3
P 2/9 6/9 1/9
{Y |X = 2} −1 1
P 19/43 30/43
2
9
+
6
9
+
1
9
= 1;
13
43
+
30
43
= 1.
X Y
m
x
= M[x] = 1 · 0, 27 + 2 · 0, 43 + 3 · 0, 30 = 2, 03
m
y
= M[y] = −1 · 0, 55 + 1 · 0, 45 = −0, 1.
X Y Y X
M[X|Y = 1] = 1 ·
2
9
+ 6 ·
2
9
+ 3 ·
1
9
=
17
9
,
M[Y |X = 2] = −1 ·
13
43
+ 1 ·
30
43
=
17
43
.
N

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