Let $W \sim \mathcal{W}_p(n, I_p) (I_p$ denodes the $p \times p$ identity matrix$)$ be a $p \times p$ standard Wishart-matrix ,$n > p$.
Determine the distribution of $tr(W)$!
From the definition, if the $C$ covariance matrix is the identity matrix, then this matix is called standard Wishart-matrix, where
$$W=\sum_{i=1}^n X_i X_i^T$$ and $X=(X_1,...,X_n)$, where $X_1,...,X_n \sim \mathcal{N}_p(0,C), C > 0$.
I have no idea how should I approach the trace of this matrix, and how to tell anything about it. Any help appreciated.