Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its finite-dimensional distributions. This is applied to ...

Now suppose F is a probability distribution on R n. There exist spherically symmetric (about the origin) random vectors X and Y whose sum X + Y has distribution F if and only if all the ...

EECE.5840 — Online and Continuing Education Id: 003318 Offering: 2 Credits: 3-3 Description Sample space, Field and Probability Measure. Axiomatic definition of Probability. Bayes' theorem. Repeated ...

In the first half of the course, we will introduce the necessary background including discrete random variables and expectations; moments and deviations; Chernoff bounds and concentration inequalities ...