I read the slides in this link : Understanding and Applying Kalman Filtering, Lindsay Kleeman
On slide 6, there is IMHO a mistake in the definition of covariance matrix of two random variables $x_1$ and $x_2$
I think it shoud be $$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\, (x_1 - \overline{x_1})(x_2 - \overline{x_2}). p(x_1,x_2)\mathrm dx_1 \,\mathrm dx_2$$ with p the joint PDF of $x_1$ and $x_2$
instead of $$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\, (x_1 - \overline{x_1})(x_2 - \overline{x_2}). p(x_1,x_1)\mathrm dx_1 \,\mathrm dx_2$$ as on slide 6.
Am I right?