Stochastic models
I made progress thinking about probability distributions today. I woke up thinking about distributions and then I started thinking about the fundamental axioms and definitions of probability and used them to derive the probabilty mass function for a binomial distribution. The proof helped me to clarify some terminology. A random variable variable is a member of set of experiments. An experiment is series of events. eg. E = {A,B} where A and B are events. An experiment is a series of events like this AAABB. this means A happened 3 times followed by B happening 2 times. A probability of a experiment is given by the amount of times of the occurance of such an experiment divided by the total size of the sample space for that experiments. An experiment with 3 trials with n(E)=2 has a sample space size of 2^3=8. The number of times of of saying obtaining 2A's in such experiment is 3C2*Pr(A)^2*(P(B))^1. This is exactly the form of probability mass function for binomial distribution. ...