## For today you should have:- Read Chapter 7.
- Homework 6.
## Today:- Convolution, including numerous examples of practical use.
- Renal tumors.
- Central limit theorem.
- Abstraction and complexity.
- Project time.
- Homework 7.
- Draft report.
## Draft report1) Turning in what you have, on time, is better than turning in something more complete, late. 2) Start with the simple stuff: one variable at a time, just characterize. 3) Don't sweep the anomalies! 4) Question, method, result, conclusion, repeat. 5) Remember the fundamentals: good presentation of numbers, tables and graphs. 6) Negative results are fine as long as the questions were reasonable. Review the project page and my "suggestions." ## Homework 61) What happens if you convolve samples from different distributions? Convolutions of exponential, normal, lognormal and Pareto distributions. Let's read Mandelbrot's theory about the prevalence of Pareto distributions. Start on page 343. 2) What happens if you add up a large number of independent random variates? The Central Limit Theorem. Does it always work? How long does it take?3) What happens if instead of adding up a bunch of independent random variables, we multiply them together?
Abstraction and complexityIn cognitive psychology and mnemonics, chunking refers to a strategy for making more efficient use of short-term memory by recoding information. More generally, Herbert Simon has used the term chunk to indicate long-term memory structures that can be used as units of perception and meaning, and chunking as the learning mechanisms leading to the acquisition of these chunks.An algebra is a set of abstract entities and operations.Example: how I (and probably you) used to do algebra. Example: how I used to do linear algebra. |

**algebra**.

**elementary algebra**, the entities are numbers and the operations are arithmetic.

**linear algebra**, the entities are matrices. Some of the operations are arithmetic and some are new (like transpose).

**," which is when we can't solve problems just because they exceed our cognitive limits.**

*complexity collapse***mathematical statistics is distribution algebra**.