ENM 500 Syllabus

This course provides a broad coverage of basic probability and statistics concepts with emphasis on random variables, probability distributions, sampling, estimation, hypothesis testing, regression and analysis of variance. Simulations are shown throughout. The software routines are used to simulate experiments which demonstrate probability phenomena and aid in the computations.

Text: Probability and Statistics with Integrated Software Routines, by Ronald Deep

Elsevier / Academic Press, copyright 2006.

Instructor: Ron Deep: Office Phone (513) 229-2238; 229-2696; Fax: 229-2698

Home 429-3263; email: (preferred)

Place: Room KL 304 in SoE; On Line with class link, or by Recording

Time: 11:00 AM – 12:15 PM Monday/Wednesday

Software: Genie

Web Link: http://academic.udayton.edu/ronalddeep/enm500.htm

Class Site: http://isidore.udayton.edu

Week / Topic / Chapter P for Problems and S for Software
1-3 / Introduction to Probability / 1 Dice:1-6,12; Coins:1-8; Cards:2,3,5,6,15
Misc 7, 10
4 / RVs, Moments, and Distributions / 2 1-5,14; Review: 1-2, 26, P:1-7 S:11-12
5 / Discrete & Continuous Distributions / 3 1-2,7-10,16,18,29-31,43,45,49,68; S: 24
4 1,4-5,7,11,14,24-36,S:1-5,12,13-14
6 / Sampling and Data Displays / 5 8-9,18-19,24,28; S:1-710-17,33
7 / Review / 1-5
7 / Mid-Term P-Set I Due / 1-5
8 / Point and Interval Estimation / 6 1-2,6,8-9;CI: 3,8-9; S: 3,7,17,24
9-10 / Hypothesis Testing / 7 1,2,9,14,18,27,30,33
10-12 / Regression / 8 1, 2,4,6,7,8,9 Misc 28, 32,36
S:2-20, 22, 33
12-13 / Analysis of Variance / 9 1-4,8,11-13, 20; S:1-15
14 / Review / 6-9
15 / Final P-Set II Due

Grading Criteria %

1 Midterm Exam 35 45 1 2 3 4 5 6

2 Problem Sets 15

1 Final Exam 50

Neatness is desired in displaying complete solutions in Word. If you miss a scheduled exam, call Ross at 229-2238 to arrange rescheduling. Try to schedule and take the missed exam before the next class.

ENM 500 Homework Problem Set 1 Due Date: Midterm Exam

1. Given RV X with density distribution f(x) = cx on [0, 3], Find:

a) c, b), E(x), c) P(1 < x < 2), d) V(X).

e) Also compute V(X) as the expected value of the second moment around the mean.

f) P(X < x) = 1/3. Determine x.

g) Generate a sample from the distribution and compare the sample mean with the computed mean using the Genie.

h) Let Y = 2X + 3 and find the expected value of Y and Y's density distribution. Also compute Y's expected value from Y's density distribution and verify 1b.

2. How many 5's are there in the numerals for the numbers from 1 to 100?

1 * 10 + 10 * 1 = 20

3. In an urn are 3 red marbles, 2 white marbles and 5 blue marbles. Three marbles are randomly selected. Let RV R be the number of red and RV W the number of white marbles. Construct the joint density for the red and white marbles. Write the conditional probability function for P(R|W = 1) and the conditional probability function for P(W|R = 2). Write the marginal density functions of
RV R and RV W. Compute E(R), E(W) and E(B) and show that the expected values of R, W and B sum to 3. R

0 1 2 3 Marginal

0 10/120 30/120 15/120 1/120 56/120

W 1 20/120 30/120 6/120 0 56/120

2 5/120 3/120 0 0 8/120

Marginal 35/120 63/120 21/120 1/120 20/120

P(R|W=1) R 0 1 2

P(R|W=1) 20/56 30/56 6/56

P(W|R=2) 0 1
15/21 6/21

E(R) = (63 + 42 + 3)/120 = 0.9; E(W) = (56 + 16)/120 = 0.6

B 0 1 2 3

P(B) 10/120 50/120 50/120 10/120

E(B) = 1 * 50/120 + 2 * 50/120 + 3 * 10/120 =180/120 = 1.5

The expected number of marbles is 3.

4. Find the number of ways that 3 bins (or nonnegative integers) can contain (or sum to) 5 items by using Canonical patterns, Inclusive/Exclusive Rule, Generating functions, and Combinatorics. Repeat if each bin must have at least one item. Then write the answers for the same problem summing to 4.

e1 + e2 + e3 = 5 (comb 7 2) = 21

(poly^n #(X 1 1 1 1 1 1 1 1) 3) à #(X 1 3 6 10 15 21 28 36 42 46 48 48 46 42 36 28 21 15 10 6 3 1)

5. Compute the following for the Standard Normal Distribution N(0, 1)

a) P(Z > 1.12) b) P(Z < - 0.96) c) P(Z > -1.50)


d) P(-1.25 < Z < 1.25) e) Find z's for P(z < Z < z) = 0.8, 0.95, and 0.99.

6. Write the integrals for computing #5 above.

ENM 500 Homework Problem Set 2 Due Date: Final Exam

Sample with replacement 50 samples from your real data or from the Genie command
(rs 50) and perform the following tasks. Include in an addendum of your results as you discuss them using Genie commands. Please do not collaborate on this homework.

1. Horizontal dot plot your data.

2. Stem and leaf your data

3. Create a histogram.

4. Boxplot your data

5. Describe your data

6. Highlight in bold the data scores between the 37th and 57th percentile.

7. Specify in most likely order the best fitting distributions.

8. (setf data-1 (re-group data (list-of 2 25))) and do a t-test on the two sets of data.

9. Use the command (setf data-2 (re-group data (list-of 5 10))). Regard your data as 10 baseball innings for 5 teams and perform a chi-square contingency test for dependence

10. Use (setf data-3 (re-group data (list-of 5 10))) and perform an ANOVA on the 5 sets of data.
Then explain the results from the command (C-anova data-3).

11. Use the command (setf data-4 (re-group (flatten data) (list-of 5 10))). Then reassign data with the command (setf x1 (first data-1) x2 (second data-1) x3 (third data-1) x4 (fourth data-1) y (fifth data-1)). Use the command

(y-hat (list x1 x2 x3 x4) y) to get the multiple linear regression equation.

Continue using the command (mlr-stats '(x1x2 x3 x4) y) and choose the best fit from the displayed criteria.

12. Use the Genie command (setf data-2 (re-group data (list-of 10 5))) to create 10 blocks of 5 data points. Compute the mean and standard deviation and create a statistical X-bar-s control chart.