If some of you are interested in the proof of the variances of the other 3 distributions that have been introduced in the lecture, you can look them up on this website:
https://proofwiki.org/wiki/Variance_of_Gaussian_Distribution
https://proofwiki.org/wiki/Variance_of_Bernoulli_Distribution
https://proofwiki.org/wiki/Variance_of_Binomial_Distribution
https://proofwiki.org/wiki/Variance_of_Gaussian_Distribution
https://proofwiki.org/wiki/Variance_of_Bernoulli_Distribution
https://proofwiki.org/wiki/Variance_of_Binomial_Distribution