Mathematical statistics is the application of probability theory
“In pure math, you prove something is true, and it stays true forever. In physics, you run an experiment, and you get a result. But in mathematical statistics, you make a decision under uncertainty. You will use this tomorrow. When your doctor gives you a diagnosis, a statistician estimated the false positive rate. When your phone translates a language, an MLE algorithm guessed the most likely sentence. When an economist says ‘inflation will be 2.5% next quarter,’ that number came from a likelihood function. mathematical statistics lecture
Mathematically, we construct bounds using probability statements: $$P(L \leq \theta \leq U) = 1 - \alpha$$ Statistics (Inductive): We are given data ($X$)