#Prob ECSE-2500 Engineering Probability, Spring 2019, Rensselaer Polytechnic Institute (Posts about homework)

Engineering Probability Homework 11 due Thu 2019-04-25

W Randolph Franklin (WRF), RPI — Thu, 18 Apr 2019 04:00:00 GMT

All questions are from the text.

Each part of a question is worth 5 points, except for 8.101.

8.1 (a-e) p 471. You decide how to generate the random samples, perhaps with Matlab or Mathematica.
8.2 (a-e).
8.49 (a-b), p 478.
8.101, p 486. 10 points.

Total: 70 points.

Engineering Probability Homework 10 due Thu 2019-04-18

W Randolph Franklin (WRF), RPI — Thu, 11 Apr 2019 04:00:00 GMT

All questions are from the text.

Each part of a question is worth 5 points.

6.68 (c), p 355. Use pmf (i).
6.92 (a-d), p 358.

Total: 25 points.

Engineering Probability Homework 9 due Thu 2019-04-11

W Randolph Franklin (WRF), RPI — Thu, 04 Apr 2019 04:00:00 GMT

All questions are from the text.

Each part of a question is worth 5 points.

6.4 (a-c), page 348.
6.23 (a-c), p 351.
6.32, p 352 (2 parts: mean, covariance).

Total: 40 points.

Engineering Probability Homework 8 due Thu 2019-04-04

W Randolph Franklin (WRF), RPI — Mon, 25 Mar 2019 04:00:00 GMT

All questions are from the text.

Each part of a question is worth 5 points.

5.103, page 298.
5.107(a), page 299.
5.114(e), page 299.
5.131(a-c), page 301. This is a chance to learn the gamma distribution.
6.1(a-d), page 348.
6.7(a-c), page 349.
6.14(a-d), page 350.

Total: 85 points.

Engineering Probability Homework 7 due Mon 2019-03-25

W Randolph Franklin (WRF), RPI — Mon, 18 Mar 2019 04:00:00 GMT

All questions are from the text.

Each part of a question is worth 5 points.

5.3 (a-c), page 288.
5.11 (a-b). Do only distribution (i).
5.17 (a-c).
5.25 (a-c), page 291.
5.41 (a-b).
5.56 (a-c), page 294.

Total: 80 points.

Engineering Probability Homework 6 due Mon 2019-03-18

W Randolph Franklin (WRF), RPI — Mon, 11 Mar 2019 04:00:00 GMT

All questions are from the text.

Each part of a question is worth 5 points.

4.38 (a-c) on page 219.
4.67 (a-d) on page 221.
4.68 on page 222.
4.69 on page 222.
4.85 on page 223.
4.90 on page 223.
4.99 a and c on page 224.
4.126 (a-b) on page 226. Assume that devices that haven't been used yet aren't failing.

Total: 75 pts.

Engineering Probability Homework 5 due Mon 2019-03-11

W Randolph Franklin (WRF), RPI — Mon, 25 Feb 2019 05:00:00 GMT

All questions are from the text.

Each part of a question is worth 5 points.

(5 points) 3.90 on p 139.
1. 3.91 on p 139.
1. 4.7 on page 215.
1. 4.11 on page 216.
1. 4.20 on page 218.

Total: 65 pts.

Engineering Probability Homework 4 due Tues 2019-02-19

W Randolph Franklin (WRF), RPI — Thu, 07 Feb 2019 05:00:00 GMT

(5 points) This is a followup on last week's first question, which was this:

Assume that it is known that one person in a group of 100 committed a crime. You're in the group, so there's a prior probability of 1/100 that you are it. There is a pretty good forensic test. It makes errors (either way) only 0.1% of the time. You are given the test; the result is positive. Using this positive test, what's the probability now that you are the criminal? (Use Bayes.)

With a lot of tests, the results are grey, and the person running them has a choice in how to interpret them: lean towards finding someone guilty (but falsely accusing an innocent person), or the other way toward finding someone innocent (but letting a guilty person go free).

Assume that in this example, the administrator can choose the bias. However the sum of the two types of errors is constant at 0.2%. (Whether that relation is really true would depend on the test.)

This question is to plot both the number of innocent people falsely found guilty and the number of guilty people wrongly let go, as a function of the false positive rate. Use any plot package. Both numbers of people will usually be fractional.
(5 pts) Do exercise 2.126, page 95.
(5 pts) Do exercise 2.127.
(5 pts) Do exercise 3.1 on page 130.
(5 pts) Do exercise 3.5.
(5 pts) Do exercise 3.13 on page 132.
(5 pts) Do exercise 3.15.

Total: 35 pts.

Engineering Probability Homework 3 due Thurs 2019-02-07 2359 EST

W Randolph Franklin (WRF), RPI — Thu, 31 Jan 2019 05:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

(5 points) Assume that it is known that one person in a group of 100 committed a crime. You're in the group, so there's a prior probability of 1/100 that you are it. There is a pretty good forensic test. It makes errors (either way) only 0.1% of the time. You are given the test; the result is positive. Using this positive test, what's the probability now that you are the criminal? (Use Bayes.)
1. Do exercise 2.59, page 87. However, make it 21 students and 3 on each day of the week. Assume that there is no relation between birthday and day of the week.
(5 pts) Do exercise 2.62 on page 88 of the text.
(5 pts) Do 2.69, but use the interval [-2,2].
(5 pts) Do 2.72.
(5 pts) Do 2.76.
(5 pts) Do 2.82.
(5 pts) Do 2.97.
(5 pts) Do 2.102.
(5 pts) Do 2.106.

Total: 50 pts.

Engineering Probability Homework 2 due Thurs 2019-01-31

W Randolph Franklin (WRF), RPI — Thu, 24 Jan 2019 05:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

(6 pts) Do exercise 2.2, page 81 of Leon-Garcia.
(6 pts) Do exercise 2.4, page 81.
(6 pts) Do exercise 2.6, page 82.
(6 pts) Do exercise 2.21, page 84.
(6 pts) Do exercise 2.25, page 84.
(6 pts) Do exercise 2.35(a), page 85. Assume the "half as frequently" means that for a subinterval of length d, the probability is half as much when the subinterval is in [0,2] as when in [-1,0).
(6 pts) Do exercise 2.39, page 86. Ignore any mechanical limitations of combo locks. Good RPI students should know what those limitations are.

(Aside: A long time ago, RPI rekeyed the whole campus with a more secure lock. Shortly thereafter a memo was distributed that I would summarize as, "OK, you can, but don't you dare!")
(6 pts) Do exercise 2.59, page 87. However, make it 35 students and 3 on each day of the week. Assume that there is no relation between birthday and day of the week.
(6 pts) Find a current policy issue where you think that probabilities are being misused, and say why, in 100 words. Full points will be awarded for a logical argument. I don't care what the issue is, or which side you take. Try not to pick something too too inflammatory; follow the Page 1 rule that an NSF lawyer taught me when I was there. (Would you be willing to see your answer on page 1 of tomorrow's paper?)

Total: 54 pts.