Теория вероятностей. Барышева В.К - 112 стр.

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Z = ϕ (X)
M[Z] =
n
X
i=1
p
i
ϕ(x
j
) =
m
X
j=1
n
X
i=1
p
ji
ϕ(x
j
).
Z = Ψ (Y )
M[Z] =
m
X
j=1
p
j
Ψ(y
j
) =
n
X
i=1
m
X
j=1
p
ji
Ψ (y
j
).
(X, Y )
D x0y f (x, y) .
X Y
M[X] = m
x
=
ZZ
D
x · f (x, y) dxdy =
+
Z
−∞
x · f
1
(x) dx
M[Y ] = m
y
=
ZZ
D
y ·f (x, y) dxdy =
+
Z
−∞
y ·f
2
(y) dy.
Z = ϕ (x)
M[Z] = m
z
=
ZZ
D
ϕ (x) · f (x, y) dxdy
Z = ϕ (X, Y )
M[Z] = m
z
=
ZZ
D
ϕ (x, y) · f (x, y) dxdy.