This is the second part of the story that I started with the previous post. Wanting to build a quick counterexample, I wondered if I can create a random variable by solving the moment problem with only finite non-zero moments. In the language of the moment problem, my sequence was such that for all greater than some number . That is, only finite elements of … Continue reading But moment picking is tricky too.
Yesterday, while trying to build a counter-example for a research problem, I started playing with the idea of designing a random variable, not by picking a vanilla distribution, but by selecting its moments myself. That is, if I pick the moments myself, can I find a distribution that has them? More formally, if I provide , is there a : probability measure such that … Continue reading Going moment-picking
This is a quick post on the different kinds of convergence that a sequence of random variable can have in a probability space. Let us suppose that we have a sequence of random variables , in a probability space . is the probability space, is the σ-algebra of measurable sets and P is the probability measure. First of all, here’s a list of the … Continue reading Kinds of convergence for sequences of random variables