Key Points

Calculus

$$\int x^ne^{ax}dx = \frac{1}{a}x^ne^{ax} - \frac{n}{a}\int x^{n-1}e^{ax}dx$$

$$\int \limits a^xdx = \frac{1}{lna} a^x + C$$

$$\int xa^x = \frac{x}{ln a}a^x - \frac{1}{(lna)^2}a^x + C$$

$$\int lnxdx = xlnx - x + C$$

Basic distribution

List of probability distributions

Goal of statistics: given a model with some unknown elements and assuming data is generated (randomly) by the model, make inference about the unknown elements.

Real-life Data $\leftrightarrow$ Truth.

Statistical Model $\leftrightarrow$ Story.

Truth = Story? Rarely.

A good (statistical) story: consistent and coherent (mathematically).

Never let the truth get in the way of a good story — Mark Twain.