E(X-μ) for X and μ Vectors: First Central Moment

[saintman4]

where X ~ N (μ, σ2)

I know that if X is random variable, the first central moment E(X-E(X)) = E(X-μ) is zero. But I would like to know if X and μ is vector. For example if X = [x1 x2] and μ = [μ1 μ2]. What is the value of E(X-μ)?



Thank you

 

[quadraphonics]

where X ~ N (μ, σ2)

I know that if X is random variable, the first central moment E(X-E(X)) = E(X-μ) is zero. But I would like to know if X and μ is vector. For example if X = [x1 x2] and μ = [μ1 μ2]. What is the value of E(X-μ)?

It's still zero, although now it's a vector of zeros. To see this, simply evaluate it component-wise and apply the scalar result you started with.