shift Archives - Infinity is Really Big

September 26, 2019September 26, 2019

Transformations of Functions

Calculus 1, Lectures 6A through 7B

Visual for the fact that $\log_{2}(2x)=\log_{2}(x)+\log_{2}(2)=\log_{2}(x)+1$ in terms of transformations of functions.

\log_{2}(2x)=\log_{2}(x)+\log_{2}(2)=\log_{2}(x)+1 — Visual for the fact that $\log_{2}(2x)=\log_{2}(x)+\log_{2}(2)=\log_{2}(x)+1$ in terms of transformations of functions.

In the 1600’s, algebra and geometry got “married” to create a new subject called analytic geometry. Insights in either branch led to insights in the other. This has been very fruitful over the years.

The symbiosis between these subjects can be especially … Read the rest

May 7, 2019May 7, 2019

Transformed Power Function Survival Models

Studying for Exam LTAM, Part 1.10

A family of transformed power function survival functions $S_{0}(t)=1-\frac{t^{p}}{\omega^{p}}$ .

S_{0}(t)=1-\frac{t^{p}}{\omega^{p}} — A family of transformed power function survival functions $S_{0}(t)=1-\frac{t^{p}}{\omega^{p}}$ .

A power function is defined by a formula of the form $f(t)=at^{p}$ for some constants $a$ and $p$ .

For certain choices of $a$ and $p$ , such a function could serve as the force of mortality for a continuous survival random variable $T_{0}$ . But it could not serve as … Read the rest