Math 464 - Prof. Kennedy - Fall 2010 - First project
This project will illustrate the concepts of density (or pmf), mean
and functions of two random variables.
You have to choose a joint density (or pmf) for the random variables X and Y.
Then choose a function g(x,y) and let Z=g(X,Y) be a new random variable.
Your choice must be non-trivial and you should
get it approved by the professor
before you start working on it. Be creative in your choice.
There are two parts to the project.
Part I
The first part is to compute the following (using all the theory we have
developed). There is no R involved in this part.
- the mean of Z
- P(a < Z < b) for some specific choice of a and b
- the cumulative distribution function (cdf) of Z
Depending on your choice of joint distribution for X and Y and your function g,
you may not be able to do these computations analytically.
You can do them numerically, i.e., numerically compute the integrals
(or sums) you need to evaluate.
Part II
The second part of the project is to do simulations in R
to (approximately) compute each of (a), (b) and (c).
The idea is to generate a large number of samples of (X,Y) and for
each sample compute Z. We can then use these samples of Z to compute
the three things in part I.
For example, to compute the mean of Z, we can just take the average of
all these samples of Z.