Теория вероятностей. Барышева В.К - 73 стр.

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Y = e
X
H M[Y ] = M[e
X
] = e
−
1 · 0.2 + e
0
· 0.3 + e
1
· 0.4 + e
2
· 0.1 =
= 0.2 · 0.3679 + 1 · 0.3 + 2.71828 · 0.4 + 7.389 · 0.1 = 2.2.
D[Y ] = D[e
x
] = M
(e
X
)
2
− M
2
[e
X
] =
=
(e
−1
)
2
· 0.2 + (e
0
)
2
· 0.3 + (e
1
)
2
· 0.4 + (e
2
)
2
· 0.1
− (2.2)
2
=
=
e
−2
· 0.2 + 0.3 + e
2
· 0.4 + e
4
· 0.1
− 4.84
= 8.741 − 4.84 = 3.9.
N
X
x
1
x
2
x
1
< x
2
p
1
= 0.2 x
1
M[X] = 3.8 D[X] = 0.16.
H X
x
1
x
2
p
2
= P (X = x
2
) = 1 − p
1
= 1 − 0.2 = 0.8.
M[X] = x
1
p
1
+ x
2
p
2
= 0.2x
1
+ 0.8x
2
= 3.8;
D[X] = (x
2
1
p
1
+ x
2
2
p
2
) − M
2
[X] = (0.2x
2
1
+ 0.8x
2
2
) − (0.38)
2
= 0.16.
2x
1
+ 8x
2
= 38
2x
2
1
+ 8x
2
2
= 146
⇒
x
1
+ 4x
2
= 19
x
2
1
+ 4x
2
2
= 73
⇒
⇒
x
1
= 19 − 4x
2
(19 − 4x
2
)
2
+ 4x
2
2
= 73
⇒
⇒ 5x
2
2
− 38x
2
+ 72 = 0 ⇒
x
0
2
= 4 x
00
2
= 3.6
x
0
1
= 3 x
00
1
= 4.6
.
x
1
x
2
x
1
x
2
x 3 4
p 0.2 0.8
N

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