There is a pretty large number of mistakes in the probability one. The covariance measures how "linearly related" two RVs are, not "how related". In the convo

There is a pretty large number of mistakes in the probability one. The covariance measures how "linearly related" two RVs are, not "how related". In the convolution formula for the sum of two RVs, you also need independence of the RVs for the convolution to be the valid approach. In the description about uncorrelated, there's a statement that "the reverse holds only for Gaussian RVs" which is not true, the word "only" needs to be taken out. (The sheet is trying to say the right thing on that one, it's just a language issue.) The N(0,1) is called a standard normal distribution, not just a normal distribution. The last equation on the sheet, for a vector normal distribution, forgets to invert the covariance matrix that appears in the exponential.