HOMEWORK: MATH/Stat 304
Homework 0
Due: Friday, 17 January
Briefly provide (in one or two paragraphs) information about yourself that will help me
get to know you. If you wish, you may let the following questions serve as a guide: why
are you taking Math/Stat 304? what is your major? what is your career goal? when did
you study multivariable calculus? Do you plan to take the first actuarial exam? (Please
eMail your response to me no later than midnight, Friday. Be certain to make the Subject
of your message: Math 304 HW 0)
Homework 1: Due: Wednesday, 22 January
Read sections 1.1, 1.2, 1.3 of Bertsekas. Solve problems 1, 2, 3, 5, 6, 7, 8. Your group is
assigned in Piazza. Watch the first two lectures of Tsitsiklis.
Homework 2: Due: Wednesday, 29 January
Study sections 1.3 and 1.4. Begin reading section 1.5. Watch the third lecture of
Tsitsiklis.
Solve: Bertsekas problems 14, 15, 16. Solve each of the following two problems:
(1) A lab blood test is 94% effective in detecting a certain disease when it is, in fact,
present. However, the test also yields a “false positive” result for 1% of the
healthy persons tested. (That is, if a healthy person is tested, then, with probability
0.01, the test result will imply that s/he has the disease.) If 0.4 percent of the
population actually has the disease, what is the probability that a person has the
disease given that the test result is positive?
(2) A drawer contains three types of disposable flashlights. The probability that a
type 1 flashlight will give more than 100 hours of use is 0.7, with the
corresponding probabilities for type 2 and type 3 flashlights being 0.45 and 0.25,
respectively. Suppose that 20 % of the flashlights in the drawer are type 1, 30 %
are type 2, and 50 % are type 3.
(a) What is the probability that a randomly chosen flashlight will give more
than 100 hours of use?
(b) Given that a flashlight lasted more than 100 hours, what is the conditional
probability that it was a type j flashlight, j = 1, 2, 3.
Homework 3: Due: Wednesday, 5 February
Study sections 1.5, 1.6 and 1.7. Review Chapter 1 in preparation for Test I. Watch the
fourth lecture of Tsitsiklis.
Solve: Bertsekas problems 49, 51, 52, 53, 59, 60. Solve MIT Tutorial I:
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041probabilistic-systems-analysis-and-applied-probability-fall2010/tutorials/MIT6_041F10_tut01.pdf
Homework 4: Due: Wednesday, 19 February
Study sections 2.1 and 2.2. Watch the fifth lecture of Tsitsiklis.
Solve: Bertsekas: chapter 2, problems 1, 3, 7, 13 and problems 2 and 4 of MIT problem
set 3
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041probabilistic-systems-analysis-and-applied-probability-fall2010/assignments/MIT6_041F10_assn03.pdf
Jakob Bernoulli
Homework 5: Due: Wednesday, 26 February Study sections 2.3, 2.4 and 2.5. Watch
the sixth and seventh lectures of Tsitsiklis. Solve:
Bertsekas: chapter 2, problems 14a, 16, 19a, 20,
21, 24. Solve problem 1 (a through g) of MIT
problem set 4.
Homework 6: Due: Wednesday, 19 March
Review chapter 2 for test 2.
Study sections 3.1, 3.2, 3.3. Watch the eighth lecture of Tsitsiklis. Solve: Bertsekas:
chapter 3, problems 1, 2, 5, 6, 7
Solve problems 1 – 3 of MIT problem set 5.
Carl Frederick Gauss (1777-1855)
Homework 7: Due: Friday, 28 March
Review sections 3.1 – 3.3. Study section 3.4 and begin reading section 4.1. Watch the
ninth lecture of Tsitsiklis. Solve: Bertsekas: chapter 3,
problems 8, 11, 12, 13, 15; chapter 4, problems 1 – 4.
Solve problem 1 of MIT problem set 6.
Prepare for Friday’s quiz.
Homework 8: Due: Wednesday, 9 April
Read section 3.5, review section 4.1 and read carefully section 4.4. Begin reading section
4.2. Solve: Bertsekas: chapter 3, problems 18, 19; chapter 4, problems 4 (again), 7,
29– 32. Prepare for Test III.
All knowledge resolves itself into probability.
- David Hume
There are times when truth hardly seems probable.
- Nikolas Boileau
Lest men suspect your tale untrue, keep probability in view.
- John Gay
The theory of probabilities is at bottom nothing but common sense reduced to calculus.
- Pierre Simon de Laplace
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