## Any ideas for a an ap stat/ ap compsci hybrid project?

I have the same teacher for the two subjects above and was wondering if you have any ideas? I was thinking of showing how the central limit theorem creates a normal curve, but im not sure that is accurate or anything.

submitted by Nevin Manimala Nevin Manimala /u/ImNoLegend27

Given a binary tree. If I randomly walk down the tree from root to a leaf (i.e. randomly chose the left or right child), what is the expected length of the path `E(P)` in terms of the tree heigh`t` h?

submitted by Nevin Manimala Nevin Manimala /u/yurttan

## What car gets an undeserved bad/good reputation despite not really being that bad/good?

I think that the 4th gen Eclipse is a little too picked on for being a bad car. Some of the issues people have with it are objective, such as the styling, and then non-issues like “the engine is boring to work on.” Sure it’s not everyone’s cup of tea but it’s a perfectly fine sports car that has plenty of daily uses and still is sporty enough to keep you from being bored.

So what are other examples of those overly or underly loved cars?

submitted by Nevin Manimala Nevin Manimala /u/cmanonurshirt

## How To Interpret lme4 Variance Parameters in 3-Level Models

The following output comes from this lme4 tutorial:

``Linear mixed model fit by REML Formula: extro ~ open + agree + social + class + (1 | school/class) Data: lmm.data AIC BIC logLik deviance REMLdev 3548 3599 -1764 3509 3528 Random effects: Groups Name Variance Std.Dev. class:school (Intercept) 2.88365 1.69813 school (Intercept) 95.17339 9.75569 Residual 0.96837 0.98406 Number of obs: 1200, groups: class:school, 24; school, 6 ``

I didn’t included fixed effects as my question is just about the random effects.

I have some intuition on how to interpret the estimated school variance. We can think of each school as having it’s own intercept, and those values follow a normal distribution. The standard deviation of that distribution is 9.76.

I have a harder time understanding what the value for class:school means. It makes sense to me to think that we also want to allow each class to also have it’s own intercept. But what is the value 1.69? Since classes are nested within schools, I would think that all 6 collections of classes have their own distribution with their own SD. What does this singular value mean?

Also, from an interpretation standpoint, since the σ_school value is much higher than the σ_class value, is the interpretation that average extraversion varies a lot between schools, but does not vary much between classes within a school?

submitted by Nevin Manimala Nevin Manimala /u/this-is-water-