#Prob ECSE-2500-01 Engineering Probability, Spring 2018, Rensselaer Polytechnic Institute (Posts about homework)

Engineering Probability Homework 11 due Mon 2018-04-30 2359 EST

W Randolph Franklin (WRF), RPI — Mon, 23 Apr 2018 04:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

All questions are from the text, starting on page 290.

Each part of a question is worth 5 points.

5.133 on page 302 (3 parts).
6.1, p 348. (4 parts)
6.3 (4 parts).
6.4 (3 parts).
6.32, p 352 (2 parts: mean, covariance).

Total: 80 points.

Engineering Probability Homework 10 due Mon 2018-04-23 2359 EST

W Randolph Franklin (WRF), RPI — Mon, 16 Apr 2018 04:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

You may use any computer SW, like Matlab or Mathematica.

Questions

All questions are from the text, starting on page 290.

Each part of a question is worth 5 points.

(10 pts) Problem 5.94 on page 298.
(5 pts) Problem 5.106 on page 298.
(25 pts) Problem 5.111 on page 299.
(10 pts) Problem 5.120 on page 300.

Total: 50 points.

Engineering Probability Homework 9 due Mon 2018-04-16 2359 EST

W Randolph Franklin (WRF), RPI — Sun, 08 Apr 2018 04:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

All questions are from the text, starting on page 290.

Each part of a question is worth 5 points.

(20 pts) Problem 5.17. (c has 2 parts.)
(15 pts) Problem 5.18.
(15 pts) Problem 5.25.
(30 pts) Problem 5.26. (d has 3 parts.)
(15 pts) Problem 5.35.
(5 pts) Problem 5.37.
(15 pts) Problem 5.56.

Total: 115 points.

Engineering Probability Homework 8 due Mon 2018-04-09 2359 EST

W Randolph Franklin (WRF), RPI — Mon, 02 Apr 2018 04:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

All questions except #1 are from the text.

Each part of a question is worth 5 points.

(15 pts) This exercise shows how the sum of independent r.v. start looking like a normal distribution.
1. Compute the pdf of the sum of 2,3,4, and 5 independent r.v. that are each U[0,1].
2. Compute the mean and standard deviation of each pdf.
3. For each sum, plot the pdf and overlay it with a plot of the pdf of the normal distribution with the same mean and standard deviation.
(30 pts) Textbook problem 5.1 on page 288 - 6 parts: a, b, c, da, db, dc.
(20 pts) Problem 5.2. (c) is 2 parts. Do all parts.
(20 pts) Problem 5.3 (c) is 2 parts. Do all parts.
(35 pts) Problem 5.12. (d) has 4 parts, giving 7 parts total.
(35 pts) Problem 5.13. (d) has 3 parts, giving 7 total.

Total: 155.

Engineering Probability Homework 7 due Thurs 2018-03-22 2359 EST

W Randolph Franklin (WRF), RPI — Thu, 08 Mar 2018 05:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

All questions are from the text.

Each part of a question is worth 5 points.

4.63 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 on page 226. Assume that devices that haven't been used yet aren't failing.
4.133 (a) on page 227.

Total: 70 pts.

Engineering Probability Homework 6 due Thurs 2018-03-08 2359 EST

W Randolph Franklin (WRF), RPI — Wed, 28 Feb 2018 05:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

All questions are from the text.

Each part of a question is worth 5 points.

4.5 on page 215.
4.8 on page 216.
4.17 on page 217.
4.33 on page 218.

Total: 55 pts.

Engineering Probability Homework 5 due Mon 2018-02-26 2359 EST

W Randolph Franklin (WRF), RPI — Mon, 19 Feb 2018 05:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

All questions are from the text.

Each part of a question is worth 5 points.

3.11a and b on page 131.
3.35 a-d on page 133.
3.53 a and b on p 135.
3.88 a-c on p 139.
3.90 on p 139.

Total: 60 pts.

Engineering Probability Homework 4 due Tues 2018-02-20 2359 EST

W Randolph Franklin (WRF), RPI — Mon, 12 Feb 2018 05:00:00 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

(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 Mon 2018-02-12 2359 EST

W Randolph Franklin (WRF), RPI — Mon, 05 Feb 2018 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 1 due Thurs 2018-01-25

W Randolph Franklin (WRF), RPI — Tue, 16 Jan 2018 16:07:17 GMT

How to submit

Submit to LMS; see details in syllabus.

Questions

(6 pts) One of the hardest problems is forming an appropriate probability model. E.g., suppose you're working for Verizon deciding how much data capacity your network will need once it starts selling the iphone. Suppose that you know that each customer will use 5GB/month. Since a month has about 2.5M seconds, does that mean that your network will need to provide only 2KB/s (correction) per customer? What might be wrong with this model? How might you make it better? (This is an open-ended question; any reasonable answer that shows creativity gets full points.)
(3 pts) One hard problem with statistics is how they should be interpreted. For example, the more iphones that are sold, the higher the national debt gets. Does this mean that the US should pay Verizon not to sell the iphone next month?
(6 pts) Do exercise 1.3 in the text on page 19.
(6 pts) Do exercise 1.6 on page 19.
(6 pts) Do exercise 1.11 on page 20.

Total: 27 pts.