Study guide for Examlet 2

Here is a non-exhaustive list of questions you should be able to answer as you prepare for the examlet.

Past chapters

See the study guide for examlet 1. (Recall from the course policies that our examlets are cumulative.)

What is interpolation?
What is a Vandermonde matrix?
What is the monomial basis?
How are the coefficients in the interpolating polynomial found?
What is the asymptotic (big-O) behavior of the error in interpolation? What does $h$ represent in the error term?
For what types of functions do you expect interpolation to work well? For which is that not the case?
What reasons exist to consider composite interpolation? (i.e. multiple polynomials on multiple adjacent intervals)

What is a random variable?
What is a distribution function? What requirements does it satisfy?
What does the law of large numbers say?
What is a sample?
What is a sample mean?
What is an expected value? What is variance?
How does the application of functions $f(X)$ affect the distribution of a random variable $X$?
What is the Box-Muller transform?
How do the samples in the law of large numbers need to be distributed?
How can you use the law of large numbers if it is difficult/expensive to sample from the random variable's distribution?
How can you use the law of large numbers if the normalization factor on the distribution of a random variable is not known?
What is the asymptotic (big-O) behavior of the error in sampling?