6/3/2019 Finalized subject list... and the software packages needed to do them.

So I think I've finally got together the things that I will be up to during this 12 week semester:

STAT 805 Computational Mathematics and Statistics: R and RStudio to do math
COMP 809 Data Mining and Machine Learning: python/ Anaconda/ Tensorflow for ML model training
ENSE 807 Digital Signal Processing: Matlab & Simulink for Signals Impulse/ Step Analysis

ASTR 800 Advanced Topics in Astrophysics: Is a readings paper, I need to read about the Universe, alot. and write a rather lengthy paper about it by the end of the semester.

STAT 805 Lecture on 6/3/2019

STAT 805 class today. We moved to Chapter 2 (normal distribution/ Gaussian) from Chapter 1 (binomial distribution)

Binomial Distribution

As the name implies its a 'two number' distribution. Two numbers meaning that the result of the experiment that conduct is either one case or the other, success or fail, heads or tail ,dark or light, day or night, good or evil, Batman or Superman.

note: this can be extended to continuous values as well. Like age (age >= 13 || age < 13) or weight (weight > 67.5 Kg || weight <= 67.5 kg). Treating it as a critical value. Then we can conduct a 'binomial trial' on a sample of n people with these critical value characteristics.

In a binomial trial of n repeated bouts in a multiverse (where the outcome of 1 Universe does not affect the other) with p being the probability of Batman coming out victorious is a success (my own Bias).

• The Experiment consists of 'n' number of repeated Trials - They fight in 'n' number of Universes.

• Each trial can result in only one of two possible outcomes - Either batman wins or Superman wins.

• The probability of a success case is constant - In every Universe batman has the same probability of winning (p=0.5).

• The trials are independent of each other - A batman win in one Universe does not affect the batman win in another Universe. (and in none of the Universe are both their moms named Martha. I think they both lose in that one)

There's no way to ace Computational Mathematics without actually getting down and dirty and playing with some RStudio. So lets get down to it and start simulating some non-Interdimensional Hero Bouts shall we?

Lets take the function: rbinom(20,5,0.5)

which tells us, if we sample 20 Universes (vector quantile), each Universe they fight (3 times) and in each Universe Batman (p = success) has a 0.5 percent chance in winning. Yields us:

[1] 2 3 3 1 4 3 2 5 3 0 3 4 2 4 3 2 3 2 2 1

[1] 3 4 1 2 4 3 1 3 0 3 1 2 2 1 0 2 3 2 3 1

[1] 2 2 3 2 1 3 3 3 2 3 2 3 1 4 2 4 4 2 1 5

Each of these numbers represents the 'n' number of Batman wins in each Universe. If we switch to n trials = 1, we get something that looks like Binary: rbinom(20,1,0.5)

[1] 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0

[2]  1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1

[3] 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1


Think of vector quantiles as your samples. Number of samples. Number of Universes or Number of kids asked to toss a coin.