Probability and Statistics ... 
... are not one and the same. The differences are not nuanced. They are Apples and Oranges.

Reading List 
I am often asked to recommend a "good statistics text." Here are a few that I refer to often. 
Rsquared ... 
... is an often misused goodnessoffit
metric, where bigger isn't always better. 
Other Measures 
Rsquared isn't the only way to
judge how well the model works. 
Curse
of Dimensionality 
Directsampling Monte Carlo
requires the number of samples per variable to increase exponentially with the number of
variables to maintain a given level of accuracy. 
convergence in
distribution 
We engineers are familiar with
convergence to a point, but what of convergence to a distribution? 
extreme value
distributions 
The largest, or smallest,
observation in a sample has one of three possible distributions. This is another
example of "convergence in distribution." 
Joint,
Marginal, and Conditional Probability 
We engineers often play fast
and loose with joint, marginal, and conditional probabilities  to our detriment. 
Correlation 
When the correlation between two variables is zero, they're not realted.
Right? Wrong! 
Outliers 
Often infuriating, these can be very informative too. 
Wrong Grid? 
Choose wisely  to avoid embarrassment. 
Bayesian Thinking 
... including an example from NDE 
InterOcular Trauma
Test 
Sometimes the best
GoodnessofFit test is the easiest. 
Central
Limit Theorem 
Why is the Average
of nearly anything always Normal ? 
Bayesian Updating 
We use Bayesian Statistics
every day without knowing it. 
Sums
of Random Variables 
Sometimes you need to know the
distribution of some combination of things. Here's an example. 
Distributional
Interrelationships 
There are myriad probability
distributions. But did you know that most are related to one another, and ultimately
related to the Normal? 
GoodnessofFit 
We engineers often use a
statistical distribution without checking to see if it's doing a good job. Here's
how to fix that. 
