MCS 342 Problem Assignments

8. Estimation

Sections to read	Topics	Problems to look at	"File" problems	Assigned problems	Due Date
6.x MCS 341 class notes	Functions of random variables	Extra credit: (1) Derive a formula for the pdf of X^Y when X and Y are continuous random variables having pdfs and P(X>0) = 1. Determine formulas and graphs for the pdfs of X+Y, Y - X, XY, Y/X, and X^Y when X and Y are independent, uniform(0,1) r.v.s .
8.1 8.2	Introduction Bias and MSE	8.12, ...	8.1	8.4	F 2/18
8.3 8.4	Common unbiased point estimators Evaluating point estimators	8.21, ...	Derive Table 8.1.	8.28, 8.29	F 2/18
8.5	Confidence intervals	8.39		8.40-8.41	M 2/21
8.6	Large-sample confidence intervals	8.51		8.50, 8.52	M 2/21
8.7	Selecting the sample size	8.60		8.58, 8.64 (Change mu₁=mu₂ to n₁=n₂.)	W 2/23
8.8	Small-sample CIs for mean and differences	8.70, 8.71		8.72, 8.76	W 2/23
7.2 8.8	Extra credit	Derive the t distribution. [Follow 7.72 or the approach in class.]			W 2/23
	Review			Find the distribution of the minimum Y₍₁₎ of a random sample from an exponential(beta) population. Also, E(Y₍₁₎) = ? V(Y₍₁₎) = ?	F 2/25
8.9	Confidence intervals for variances	8.81	8.84	8.82	F 2/25
7.2	F distribution	7.13, 7.15, 7.18 Extra credit: 7.73			F 2/25

"Problems to look at" are not to be turned in if they're not extra credit problems.

Keep "file" problems in a file for occasional inspection.

Turn in "assigned problems" on the given due date at the start of class.

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."