Essays for mathematics for mathematics's students

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Decision Theory - Essay - Mathematics

Enough probability; we have what we need now to start doing statistics. “Decision theory” is about how to behave optimally under uncertainty, and as such provides a nice backbone for the various statistical procedures we’ll be looking at.

Central Limit Theorem - Essay - Mathematics

Paninski, Intro. Math. Stats., October 5, 2005 35 probability, ZN !P Z, if P(|ZN − Z| > !) ! 0 as N ! #. (The weak LLN is called “weak” because it asserts convergence in probability, which turns out to be a somewhat “weak” sense of stochastic conv...

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Connectedness Continues - Essay - Mathematics

Wanted to generalize theorems about continuous functions to general metric spaces. Had to generalize closed intervals, which is compactness. From last time, E compact and f continuous ) f(E) is compact. Also, E connected and f continuous