Homework

• HW 1 (due at class time on Sep. 17, but grace period until 10 PM on 9/18)
• solutions for HW 1
  • The 5 parts graded: 3, 4, 5, 7, 8.
  • Here is a summary of the scores (for 30 students in both of my STAT 544 sections this semester):
    • 14 students got scores in the interval [19.25, 20],
    • 13 students got scores in the interval [13.6, 18.1],
    • 3 students got scores in the interval [2.5, 11.6].
    The median is 17.85 (out of 20, so 89.25%).
  • Here are some comments about the grading.
    • Some students wrote expressions like

      P( A ∪ B )^C

      instead of

      P( (A ∪ B )^C ).

      (One set of parentheses is needed for the event (the complement of A union B), and another set of parentheses is needed for the probability function.) I just deducted 0.1 point for this use of bad notation.
    • A lot of you lost points (or at least a fraction of a point) for not giving adequate justification for your final answers. With simple problems like 2 and 4, not a lot of explanation is needed, but for more complex problems like 3 and 5, some sort of explanation should be given for where the numerator counts are coming from.
    • In the mathematical portion of your solutions, P should be reserved for the probability function. Don't use P for an event, and don't write something like P = 1/720. (It's okay to have P(E) = 1/720, given that E has been properly defined, since here P is used as the probability function, but in P = 1/720, P is being used as a specific probability, and not as the probability function.) Similarly, reserve the use of S to denote the sample space (don't use it for any other event).
    • A lot of students wrote P(E) without ever defining E. I didn't count off (this time) for such minor abuses of notation, but I may be more picky in the future.
  • (A lot of students could have earned more partial credit if they had properly defined the events they used and better explained their method of solution.)
• Extra Ch. 1 Problems (not to be graded)
• solutions for Extra Ch. 1 Problems
• Extra Ch. 2 Problems (not to be graded)
• solutions for Extra Ch. 2 Problems
• HW 2 (due at class time on Sep. 24, but grace period until 10 PM on 9/25)
• solutions for HW 2
  • The 5 parts graded: 1(a), 3, 4, 5, 7.
  • Here is a summary of the scores:
    • 16 students got scores in the interval [18.5, 20],
    • 3 students got scores in the interval [17.25, 17.95],
    • 4 students got scores in the interval [16.05, 16.4],
    • 3 students got scores in the interval [15.4, 15.65],
    • 4 students got scores in the interval [6.6, 13.25].
    The median is 18.725 (out of 20, so 93.625%).
• Extra Ch. 3 Problems (not to be graded)
• solutions for Extra Ch. 3 Problems
• HW 3 (due at class time on Oct. 1, but grace period until 10 PM on 10/2)
• solutions for HW 3
  • The 5 parts graded: 1, 2, 3, 5(a), 5(c).
• Extra Ch. 3 and Ch. 4 Problems (not to be graded))
• solutions for Extra Ch. 3 and Ch. 4 Problems
• HW 4 (due at class time on Oct. 8, but grace period until 10 PM on 10/9)
• solutions for HW 4
  • The 5 parts graded: 1, 2, 4(a), 4(c), 5.
  • Here is a summary of the scores (for 29 students in both of my STAT 544 sections this semester):
    • 5 students got scores in the interval [18.95, 19.9],
    • 7 students got scores in the interval [16.95, 18.35],
    • 5 students got scores in the interval [15.2, 16.35],
    • 8 students got scores in the interval [10, 14.2],
    • 4 students got scores in the interval [6, 8.5].
    The class median is 15.95 (out of 20, so 79.75%).
• Extra Ch. 4 Problems (not to be graded)
• solutions for Extra Ch. 4 Problems
• HW 5 (due at class time on Oct. 15, but grace period until 10 PM on 10/16)
• solutions for HW 5
  • The 5 parts graded: 1, 2, 3, 4(a), 4(c).
  • Here is a summary of the scores (for 28 students in my two STAT 544 sections who bothered to submit a paper):
    • 6 students got scores in the interval [19.5, 20],
    • 12 students got scores in the interval [15.65, 18.4],
    • 5 students got scores in the interval [13.55, 14.8],
    • 5 students got scores in the interval [6.5, 12.05].
    The median is 16.3 (out of 20, so 81.5%).
  • Here are some comments about the grading.
    • Some students wrote expressions like

      P( A ) ∪ P( B )

      instead of

      P( A ∪ B )

      ... but a union of probabilities doesn't make sense.
    • Some used X (or A) as both a random variable and an event in the same problem ... it can't be both.
    • Some did a "brute force" solution for Problem 3. Besides lacking elegance, such a method doesn't "scale up" nicely. If instead of starting with 3 black and 3 white balls, we started with 30 of each, and if instead of counting the number of draws to get the 2nd black ball, we counted the number of draws to get the 20th black ball, my method of solution isn't too much more work, but a "brute force" solution is a lot more work.
    • Please staple your sheets together!
    • Please draw boxes around your final answers!
• Extra Ch. 4 and Ch. 5 Problems (not to be graded)
• solutions for Extra Ch. 4 and Ch. 5 Problems
• HW 6 (due at class time on Oct. 22, but grace period until 10 PM on 10/23)
• solutions for HW 6
  • The 5 parts graded: 2, 3(a), 3(b), 3(c), 3(d).
  • Here is a summary of the scores:
    • 9 students got scores in the interval [19.45, 20],
    • 5 students got scores in the interval [18.65, 19.1],
    • 12 students got scores in the interval [14.5, 18],
    • 4 students got scores in the interval [8.7, 12.25].
    The class median is 17.75 (out of 20, so 88.75%), out of the 30 papers submitted (one student did not submit a paper on time this week).
• Extra Ch. 5 Problems (not to be graded)
• solutions for Extra Ch. 5 Problems
• HW 7 (due at class time on Oct. 29, but grace period until 10 PM on 10/30)
• solutions for HW 7
  • The 5 parts graded: 1(a), 1(b), 2, 3, 4.
  • Here is a summary of the scores:
    • 11 students got scores in the interval [19.5, 20],
    • 6 students got scores in the interval [17.7, 19],
    • 9 students got scores in the interval [12.75, 16.65],
    • 3 students got scores in the interval [4.45, 11.1].
    The class median is 18.95 (out of 20, so 94.75%), out of the 29 papers submitted (two students did not submit a paper this week).
  • Here are some comments about the grading.
    • Some students are still arriving at pdfs which take negative values, and cdfs which take values outside of the range [0, 1], or which decrease instead of increase over the distribution's support. Also, some arrive at negative values for expectations when the random variables do not take negative values. So, it's obvious that some need to give more consideration as to whether or not their answers are even sensible.
    • Over half of my 544 students do a pretty good job with the HW each week, but some need to start working much more carefully. While it's great that some who got off to a bad start this semester have been doing much better recently, it's disturbing that some who were doing rather well have now had two or three bad HW submissions in a row. In some cases it seems like poor calculus skills are to blame.
• Additional Extra Ch. 5 Problems (not to be graded)
• solutions for Additional Extra Ch. 5 Problems
• HW 8 (due at class time on Nov. 5, but grace period until 10 PM on 11/6)
• solutions for HW 8
  • The 5 parts graded: 1, 2, 3, 4(a), 4(d).
  • Here is a summary of the scores:
    • 7 students got scores in the interval [19.55, 20],
    • 12 students got scores in the interval [17.6, 19.15],
    • 4 students got scores in the interval [15.6, 16.15],
    • 7 students got scores in the interval[7, 14].
    The class median is 18.05 (out of 20, so 90.25%), out of the 30 papers submitted (one student did not submit a paper this week).
• Extra Ch. 6 Problems (not to be graded)
• solutions for Extra Ch. 6 Problems
• HW 9 (due at class time on Nov. 12, but grace period until 10 PM on 11/13)
• solutions for HW 9
  • The 5 parts graded: 1(a), 1(c), 2, 3, 4(a).
  • Here is a summary of the scores:
    • 20 students got scores in the interval [18, 20],
    • 7 students got scores in the interval [14.9, 17],
    • 3 students got scores in the interval [11.3, 13].
    The class median is 19 (out of 20, so 95%), out of the 30 papers submitted (one student did not submit a paper this week).
• Additional Extra Ch. 6 Problems (not to be graded)
• solutions for Additional Extra Ch. 6 Problems
• HW 10 (due at class time on Nov. 19, but grace period until 10 PM on 11/20)
• solutions for HW 10
  • The 5 parts graded: 2, 3(a), 3(b), 4(a), 4(b).
  • Here is a summary of the scores:
    • 5 students got scores in the interval [19.8, 20],
    • 5 students got scores in the interval [19, 19.35],
    • 13 students got scores in the interval [14.95, 18.35],
    • 5 students got scores in the interval [11.5, 13.45],
    • 3 students got a score below 10.
    The median score is 16.65 (out of 20, so 83.25%), out of the 31 papers submitted.
• Extra Ch. 7 Problems (not to be graded)
• solutions for Extra Ch. 7 Problems
• HW 11 (due at class time on Dec. 3, but grace period until 10 PM on 12/4)
• solutions for HW 11
  • All parts graded for this assignment.
  • Here is a summary of the scores:
    • 16 students got scores in the interval [19.7, 20] (including 5 scores of 20),
    • 11 students got scores in the interval [15.9, 19],
    • 3 students got scores in the interval [9.9, 14.3].
    The median is 19.75 (out of 20, so 98.75%), out of the 30 papers submitted.
• Additional Extra Ch. 7 Problems (not to be graded)
• solutions for Additional Extra Ch. 7 Problems
• more solutions for Additional Extra Ch. 7 Problems (Note: In the 9th Ed. of Ross, Proposition 4.2 is on pp. 305-306 (instead of p. 323).)
• HW 12 (due at class time on Dec. 10, but grace period until 10 PM on 12/11)
• solutions for HW 12
  • The 5 parts graded: 1, 2, 3, 4(a), 4(b).

Presentation of Homework Solutions

• Use paper which is approximately 8.5 inches by 11 inches.
• Staple (as opposed to paper clipping or dog-earing) sheets together in upper left corner.
• Present solutions in proper order. (E.g., solution for Problem 1 should come before solution for Problem 2, and solution for part (a) should come before solution for part (b).)
• Draw boxes around or highlight your final answers (or you can use a bold font if you type your work).
• Give just one answer for each part --- don't hedge by indicating that the answer is either this or that.
• Unless problems are truly trivial, provide adequate justification for your answers.
• Express numerical answers exactly, or else round to three significant digits. (The following numbers have three significant digits: 20.8, 0.208, and 0.00208. The numbers 0.020 and 0.002 have only two and one significant digits.) If an approximation formula is used to obtain a numerical answer, don't indicate too much accuracy by giving a lot of significant digits. (Often two significant digits are all that are warrented for an approximate answer, but follow any specific guidelines that I give in class or with the assignments.)
• Unless it's stated otherwise, don't express answers as messy expressions that need to be evaluated (e.g., involving binomial coefficients or integrals). For things like probabilities and expected values, I generally want numerical answers. (For HW 1 I want each answer given in numerical form (either as a fraction or in decimal form (possibly rounded to 3 significant digits (which is not necessarily the same thing as rounding to the nearest thousandth)).)
• Unless they are defined for you in the statement of a problem, be sure to clearly define any events and random variables that that you use. (For example, for part 1(a) of HW 2 you might define D to be the event that all three men get off on different floors, for part 1(b) you might define E_i to be the event that the elevator will stop at floors i, i+1, and i+2, and for Problem 2 of HW 2 you might define A to be the event that the selected object is amber, and B be the event that the selected object is a ball .)

Late HW Policy (and Submission of Papers Outside of Class)

• Typically, you can turn in homework up until 10 PM on the night after it is due (so you can have an extra 24 hours after the class is over). You can assume this grace period is in effect unless I announce otherwise.
• When dropping off late HW papers, take them to my office in Nguyen Engineering Building, putting them under my door (my office is room 1706).
• If you fax your paper (to (703) 993-1700), send me an e-mail indicating that you did, so that I can go fetch your paper from the department's fax machine.
• Never e-mail me your solutions --- I want a paper copy that I can carry around and grade.
• If you fax your paper, or drop it off, and for whatever reason I don't get it, then I won't give you any credit. So the best plan will be to always turn in your paper to me in the classroom on the Wednesday that it is due (but it is usually safe for you to put your paper under my office door --- I don't know of any instances when students have done so and I didn't get the paper).

Academic Integrity