Expressing a Binomial as the sum of two Poisson random variables, and working on automatic data science project

## Morning Probability HW

After getting organized in enumerating more of the homework problems from the two Carnegie Mellon stats courses, I spent some time working through this problem which poses:

Assume $X \sim \text{Poisson}(\lambda)$ and $Y \sim \text{Poisson}(\mu)$, and that $X, Y$ are independent. Let $n$ be a positive integer. Show that $(X \vert X+Y = n) \sim \text{Binomial}(n, p)$ with $p = \frac{\lambda}{\lambda + \mu}$.

it was a nice way to review conditional probability, joint distribution functions and play with Poisson random variables a bit, and also to hammer home the point that random variables can be manipulated, transformed, and expressed in terms of other random variables. I look forward to being fully caught up in the homework so that I can begin completing the exercises in the material I've studied in the book on expectation and then move onto inequalities and the convergence of random variables.

## Afternoon automatic data science project work

This afternoon I resumed work on the automatic data science project. I'm getting started with a (seemingly) simple problem: given a labeled dataset for a classification problem along with information about which columns are the inputs, outputs, and what kind of variables they are, produce a notebook that loads the dataset, preprocesses it and applies cross validation with a logistic regression model. The notebook should explain its reasoning for doing each kind of preprocessing operation (e.g one-hot encoding of categorical variables, standardization of quantitative variables) as it goes.

I figure this is just enough to define the bones of the project and will serve as a good first milestone. The very first thing I'm doing is hand writing what I'd like the output to look like for kaggle's titanic dataset based on my learnings from previous attempts, and from there I'll start working on how to automate that process so that it could work for kaggle's forest cover type dataset.

After that, I can start making it a bit more rich (exploratory analysis, trying out more models) and work on inferring variable types based on the dataset so that ideally the tool could work completely hands-free with a new dataset. I had started working on this sub-problem first a few weeks ago and have made some progress, but have decided it is a bit too low-level and would rather get the bones in place first.