It's self education, and I can't understand how to prove this task:
Let $\mathbf X_1, \mathbf X_2,..., \mathbf X_N$ be a sample of size $N>p$ from a continuous $p$-variate random vector $\mathbf X$ with density function $f(\mathbf x)$, and let $\mathbf S$ be the sample covariance matrix. Show that $\mathbf S$ is positive definite with probability $1$.
$\mathbf S$ is positive definite when for all non-nullable vector $\mathbf z$ we have $\mathbf z\mathbf S\mathbf z > 0$.
Thank you in advance)