Expectation involving normal random matrices

53 Views Asked by At

Let $X=(x_{ij})\in\mathbb{R}^{n\times p}$ with $p>n$. Assume $x_{ij}$ are independent $N(0,1)$ random variables.

My question is: how to find $E\left(X^{T}(XX^{T})^{-1}X\right)$?