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回答 (1)
2021-04-01 5:52 pm
X,Y are joint Gaussian,
∴ aX + bY is Gaussian, fo any constants a, b.
E[aX+bY] = aE[X] + bE[Y]
Var[aX+bY] = a^2 Var[X] + b^2 Var[Y] + 2abρ√(Var[X]Var[Y])
Z = -3X + 5Y
∴ E[Z] = (-3)(1)+(5)(-3) = -18
Var[Z] = (-3)^2 (2) + 5^2 (4) + 2(-3)(5)ρ√(2×4)
= 118 - 60√2 ρ
ρ = 0 ==> Var[Z] = 118
ρ = -0.1 ==> Var[Z] = 118 + 6√2
∴ aX + bY is Gaussian, fo any constants a, b.
E[aX+bY] = aE[X] + bE[Y]
Var[aX+bY] = a^2 Var[X] + b^2 Var[Y] + 2abρ√(Var[X]Var[Y])
Z = -3X + 5Y
∴ E[Z] = (-3)(1)+(5)(-3) = -18
Var[Z] = (-3)^2 (2) + 5^2 (4) + 2(-3)(5)ρ√(2×4)
= 118 - 60√2 ρ
ρ = 0 ==> Var[Z] = 118
ρ = -0.1 ==> Var[Z] = 118 + 6√2
收錄日期: 2021-05-04 00:43:32
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20210401063458AAoC3o9