Теория вероятностей. Барышева В.К - 75 стр.

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A, . . . , D 1 2 3 4 5 6
p 1/6 1/6 1/6 1/6 1/6 1/6
M[A] = M[B] = M[C] = M[D] =
1
6
· (1 + 2 + 3 + 4 + 5 + 6) = 3.5
M[A + B + C + D] = M[A] + M[B] + M[C] + M[D] = 14
M[A
2
] = M[B
2
] = M[C
2
] = M[D
2
] =
= 1/6 · (1
2
+ 2
2
+ 3
2
+ 4
2
+ 5
2
+ 6
2
) =
91
6
D[A] = D[B] = D[C] = D[D] =
91
6
− (3.5)
2
=
91
6
−
49
4
=
35
12
D[A + B + C + D] = D[A] + D[B] + D[C] + D[D] =
= 4 ·
35
12
=
35
3
= 11.7
σ[A + B + C + D] =
√
11.7 = 3.415.
N
x
p A
A M[X], M[2X + 4],
D[X], D[5X − 6], σ[X].
A = 0.12; M[X] = 2.41; M[2X + 4] = 8.82;
D[5X − 6] = 22.5; σ[X] = 0.95.
x −1 0 1 2
p 0.3 0.1 0.5 0.1
X
3
M[Y ] = 1, D[Y ] = 6.2.
f
1
(x) =
0, x 6 0
(x/18), 0 < x 6 6
0, x > 6
f
2
(x) = (1/2) exp{−|x|}

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