In robotics literature, we observe endless number of equations written in probabilities. I’d like to point out few ones which I found typically useful to remember. You will find all these in any book with probability theory.
depending on whether the random variable is a continuous or discrete variable.
One can see that the law of total probability is a variant of marginalization, which states following:
for discrete or continuous random variable , respectively.
One will also get to use/see the product rule a lot.
Note that the joint distribution of can be expressed in two different equations as shown above. And whenever you see a conditional distribution, remember that it can also be expressed differently using Bayes rule.