I'm a bit of a novice at maths and want to learn more about algebraically manipulating likelihoods in statistics. There are a lot of equations that involve taking the product of a set of values given a model.
I know a few rules for manipulating sigma-notation (e.g., here and here).
- What are the basic rules for manipulating sequences of products (i.e, $\prod_{i=1}^{I} ... $)? Is there a web page that you could direct me to?
e.g.,
- $\prod_{i=1}^{I} x_i$
- $\prod_{i=1}^{I} x_i y_i$
- $\prod_{i=1}^{I} a + b x_i$
- $\prod_{i=1}^{I} \exp x_i$