EECS 461: Probability and Statistics
Daily Schedule
  Spring 2007



Instructor:  Prof. Erik Perrins
Office: 2044 Eaton Hall
Office hours: MW 1:45–2:45, 4:15-5:00.  Drop-ins at other times are always welcome but are best scheduled via e-mail.
Office phone: 864-7370/864-7770
E-mail: esp "at" eecs.ku.edu


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  HW is assigned on the dates shown.  It is due at the beginning of the next lecture period.


Day
 Date
 Quiz/Exam
 Reading Assignment
 HW Set
 HW Due Next Lecture
Wed
 01/24
Sec 1.1-1.3
 1
 1.1.9, 1.1.11
Mon
 01/29
Sec. 1.3, 1.4
 2
 1.3.1, 1.3.7, 1.4.3, 1.4.12
Wed
 01/31
Sec. 1.5, 1.6
 3
 1.5.5, 1.5.7
Mon
 02/05
Sec. 1.6, 1.7
 4
 1.6.1, 1.6.2, 1.7.14, 1.7.15
Wed
 02/07
Sec. 2.1-2.3
 5
 2.2.3, 2.2.11
Mon
 02/12
 SQ #1
 Sec. 2.3-2.4
 6
 2.3.1, 2.3.6
Wed
 02/14
Sec. 2.4-2.6
 7
 2.5.15, 2.5.16, 2.6.5
Mon
 02/19
Sec. 2.7-2.9
 8
 2.7.7
Wed
 02/21
Sec. 2.10-2.12
 9
 2.9.13, 2.10.2
Mon
 02/26
Sec. 2.13, 2.14 10
 Supp. Exer. 2.20, 2.14.14, 2.14.19, C1 (due 3/5)
Wed
 02/28
Sec. 3.1-3.3
 11
 3.1.4, 3.1.14, 3.2.5
Mon
 03/05
 SQ #2
 Sec. 3.4, 3.5 12
 3.2.9, 3.4.1, 3.4.3
Wed
 03/07
Sec. 3.5
 13
 3.4.9, 3.4.13, 3.5.6, 3.5.25
Mon
 03/12
Sec. 3.6-3.8
 14
 3.6.13
Wed
 03/14
 Midterm  Exam [all of the above]
 ---
 C2



SPRING BREAK

Mon
 03/26
Midterm solutions

Wed
 03/28
Sec. 4.1-4.3
 15
 4.3.1, 4.3.3, 4.3.9, 4.3.14
Mon
 04/02
Sec. 4.4-4.7
 16
 4.4.5, 4.5.7
Wed
 04/04
Sec. 4.8-4.10
 17
 4.7.3, 4.8.4
Mon
 04/09
Sec. 4.11, 4.12
 18
 4.11.1, 4.11.15
Wed
 04/11
Sec. 4.13, 4.14
 19
 4.13.1, 4.13.5
Mon
 04/16
Sec. 4.15
 20
 4.14.1, 4.14.15, 4.15.2, C3
Wed
 04/18
Sec. 4.16
 21
 4.15.15, 4.16.7
Mon
 04/23
Sec. 5.1, 5.2
 22
Wed
 04/25
 SQ #3
23
 5.2.6, 5.2.13, 5.2.14, C4
Mon
 04/30
Sec. 5.3, 5.4
 24
 5.3.1, 5.3.10 Expectation Problems
Wed
 05/02
Sec. 5.5, 5.6
 25
 5.5.4, 5.5.12, 5.5.16, C5
Mon
 05/07
Sec. 5.6, 5.7
 26
 5.7.1, 5.7.3
Wed
 05/09
course review
 ---
Wed
 05/16
 Final Exam




C1 [Due 03/05]
Generate n pseudo-random uniformly distributed numbers on the interval (0,1), plot the (bar graph) frequency histogram (10 cells), and then plot the stair-step cumulative distribution function as a line graph (not as a bar graph) for (a) n=100 and (b) n=900.  For both graphs, insert proper abscissa values (0.1,...).

C2 [Due 04/02.]
Work Problem 3.4.8 in Kinney's book.

C3 [Due 04/23]
Generate 1200 uniform random numbers X on (0,1).  Form a sample value of a random variable Z by summing the first 12 samples of X and subtracting the number 6.0, and so forth to yield 100 samples of Z.  Plot the histogram and cumulative distribution for Z. (This exercise demonstrates the  Central Limit Theorem.)

C4 [Due 05/02]
Generate 100 sample values each of X and Y as independent uniform random variables on (0,1).  Form W and Z from the Box-Muller formulas given by:
         W = sqrt(-2.0*ln(X))*cos(2*pi*Y)
         Z = sqrt(-2.0*ln(X))*sin(2*pi*Y)
Plot histograms (100 points each, 10 cells) and cumulative distribution functions for W and Z.

C5 [Due 05/10]
In C3 and C4 you generated three data sets, with 100 sample values in each set (Z in C3, and W and Z in C4).  Compute the sample mean and sample variance for each data set (in other words, crunch each data set down to a sample mean and sample variance).  We already suspect that each of these random variables (Z, W, and Z) has zero mean and unit variance.  Now we will test these hypotheses.  Based on your sample means and variances, form 95% confidence intervals for the means and variances of Z (in C3) and W and Z (in C4).  Using a null hypothesis that the mean is zero and the variance is one, calculate p values for all three cases and compare these to the 5% level of significance, identifying whether the hypotheses are accepted or rejected.



Answers to Even-Numbered Problems:

1.4.12: 9/44
1.6.2: 2p2 - p4
1.7.14: 27/95
2.3.6: mean=121/81, var=4556/6561
2.5.16: 120
2.10.2: 28/435
Supp. Exer. 2.20: a) 0.3528, b) 116
3.1.4: a) 4/5, b) 2/75
3.1.14: 1/5
3.5.6:  a) 0.1056, b) 0.01
4.3.14: a) 1/3, b) 1/3
4.8.4: lambda/(lambda - t)
4.15.2: a) t7 = -2.13 (accept Ho), b) z = -2.04 (reject Ho), c) F(7,9) = 0.12, T11 = -0.9738 (accept Ho)
5.2.6: b) 12x(1-x)2, 0 < x < 1, 12y(1-y)2, 0 < y < 1, c) 43/256
5.2.14: b) 0.25*ln(2)
5.3.10: a) k=10, b) f(x) = 10x/3(1-x3), g(y) = 5y4, c) 3y2/(1-x3)
5.5.12: not independent
5.5.16: 1/2