* Probability:The theory of chance :Penn:statistics:
Learn course structure and how to start. Pre-Course Video Lectures: Introductory Material and Background Review 0. Preamble - Prelude to a theory of chance The flowering of a mathematical science [07:21] The requisite background [04:48] Table d’hote: the topics of the course [03:26]
Towards an axiomatic theory of chance
From side information to conditional probabilities.
Independence-the warp and the woof in the fabric of chance
From polls to bombs and queque-enter the binomial and the Poisson.
The fabulus limit laws-the bell curve pirouettes into the picture.
Topics->Tableaux->{prelude, body, dessert}
On how to study mathematics [03:48] The amazing aspects of fluctuations and the hot hand phenomenon The tosses of a coin [09:31] n := number of tosses
r := length of success run
Sn(r) := probability that at least one success run of length r occurs on or before the n-th trial.
r S50(r) S100(r) 2 1.00 1.00 3 0.98 1.00 4 0.83 0.97 5 0.55 0.81 6 0.31 0.55 7 0.17 0.32 8 0.08 0.17 9 0.04 0.09 10 0.02 0.04
The hot hand phenomenon [08:22] Summary of Tableau 1, Part 2 [02:12] 2. Combinatorial elements Finite sets, ordered samples, subpopulations [11:56] Sampling with replacement, powers [08:36] Sampling without replacement, falling factorials [12:15] Subpopulations, binomial coefficients [07:25], Test your understanding, card problems [10:37] Summary of Tableau 2, Part 1 [01:06], Basic properties of binomial coefficients Alternative forms for the falling factorial [04:19], Equivalent expressions for binomial coefficients, algebraic and combinatorial arguments [04:11] Pascal’s triangle [10:07] The binomial theorem [03:55] Test your understanding, binomial identities [02:38] Summary of Tableau 2, Part 2 [02:27]