MCS 341 Problem Assignments

6. Functions of Random Variables

Sections to read	Topics	Suggested problems	Assigned problems	Due Date
Class notes	Sum of a random number of r.v.s	Extra credit (ps) (pdf)		F 12/3
6.1 6.2 6.3	Introduction Finding the probability distribution of a function of random variables The method of distribution functions	6.1, 6.7	6.2, 6.6, 6.9	F 12/3
	Simulation	6.13, 6.17	6.14	M 12/6
	Simulation	Extra credit: Prove the Fundamental Theorem of Simulation
6.4	The method of transformations	6.19	6.22, 6.24
6.5	The method of moment-generating functions	6.35, 6.37, 6.49	6.34, 6.40, 6.46	W 12/8
6.6	Multivariable transformations using Jacobians	Extra credit: 6.54		F 12/10
Class notes	Sums and quotients of random variables	Handout theorems	Let X and Y be independent normal r.v.s having mean 0 and the same variance. Derive the pdf of Y/X.	F 12/10
Class notes	Differences, products, and powers of r.v.s	Extra credit: Determine the distributions of X - Y, XY, and/or X^Y if X and Y are independent.		M 12/13
6.7	Order statistics	6.59, 6.61 Extra credit: 6.62	6.58, 6.60, 6.65	M 12/13

"Suggested problems" are not to be turned in if they're not extra credit problems.

Homework rules

Students are encouraged to discuss course topics with one another. On assigned work, though, you are expected to do the work on your own. Your discussion with other students should be confined to matters related to understanding the problems and general approaches to doing problems, and you should acknowledge those who help you in this way. You should not collaborate on problem solutions unless directed otherwise.

Acknowledge your sources (people and texts).
In nontrivial problems, show how you get your answers.
Turn in neat, well-written solutions, not messy first drafts. Trim "fringes." Staple multiple-page submissions.
Do not copy collaborative solutions; write up solutions in your own words.
Turn in homework on time. Each class day late reduces the possible points by 33%.
Do extra credit problems entirely on your own. Turn in solutions separately from regular homework.

Honor pledge: "On my honor, I pledge that I have not given, received, or tolerated others' use of unauthorized aid in completing this work."