Homework
HOMEWORK 1
D&S: Section 1.4: 5,7,8; Section 1.5: 9,10,11,12,13,14 (Solutions: problem 14: (a) Anti-A: 0.38 and Anti-B: 0.16, (b) 0.04); Section 1.6: 4,5,6 (solutions: problem 4: 1/7; problem 6: 1/4); Section 1.7: 5,6,8,10 (Solutions: problem 6: 0.01543; problem 8: 360/2401; problem 10: solution for (a), (b) and (c): r/100).
D&S Section 1.8: 4,6,7,8,9,11,13,18 (solutions: problem 4: 1/10626; problem 8: n/C{n,k}. problem 18: approx 0.0143). Section 1.9: 3,5,8 (solutions: problem 8: 0.0324). Section 1.10: 7,8,10,12,13 (Solutions: problem 10:0.5).
PLEASE TURN IN THE FOLLOWING PROBLEMS ON THURSDAY OCTOBER 8th: Section 1.5: 12 and 13. Section 1.8: 8,9. Section 1.9: 8. Section 1.10: 13.
HOMEWORK 2
D&S Section 2.1: 1,2,3,5,6,9,11,12 (problem 2: 0; problem 6: 2/3); Section 2.2: 2,4,7,10,11,12,13,16,22,23 (problem 4: (1/6)^3, problem 10:(p_3+p_4+p_5)/(p_1+p_2+p_3+p_4+p_5), with p_j=(5 choose j) x 0.25^j (0.75)^(5-j); problem 12: (a) 1/4 (b) 11/24; problem 16: 379/2187.Kadane: Section 2.3.2: problems 2 and 3.
D&S Section 3.1: 2,5,6,7,8,10 (Problem 2: 1/15, problem 6: 0.1509, problem 8: 0.1330, problem 10: (b) 1/3).
Section 2.3: 4,5,6,7 (problem 4: approx 0.00019, problem 6: (a) 96/97 (b) 64/65).
You need to turn in the following problems on Tuesday 10/20 (in class): Section 2.1: 12; Section 2:2: 16, 22, 23. Section 2.3: 5. Kadane, section 2.3.2: problem 2.
HOMEWORK 3
Kadane: Section 2.4 problems 3 and 6.
D&S Section 3.1: 7,8,9,10,11 (Solutions: problem 8: 0.1330, problem 10: (b) 1/3). Section 3.2: 3,4,5,8,9,10,13 (Solutions: problem 4: (a) 3/7; (b)37/56; problem 8: (a) 2 (b) exp(-2)-exp(-4); problem 10: (a) 1/2; (b) 1-(1/2)^(1/2). Section 3.3: 3,4,5,6,8,9,17(a) (Solutions: problem 4: (a) 0.1, (b) 0.1, (c) 0.2, (d) 0, (e) 0.6, (f) 0.4, (g) 0.7, (h) 0, (i) 0, (j) 0, (k) 0, (l) 0.2; problem 8: z^2 for 0< z< 1 and 0 otherwise).
D&S Section 3.4: 3,4,5,8,10 (Solutions: problem 3: (a) 1/40 (b) 1/20 (c) 7/40 (d) 0.7; problem 4 (a) 3/2 (b) 3/8 (c) 1/8 (d) 1/2 (e) 0; problem 5: (a) 5/4; (b) 79/256 (c) 13/16 (d) 0; problem 8: (a) 5/78; (b) 25/78; (c) y(9+y)/52 (d) (3x^2+2y)/156); problem 10: (b) 1/3).
D&S Section 3.5: 2,3,4,6,7,8,10,11,13,15 (Solutions: problem 2: (a) (2x+3)/15 (b) (1+y)/10; problem 3: (b) they are independent; problem 4 (a) f(x)=15 x^2(1-x^2)/4 and f(y) = (5(1-y)^{3/2})/2 (b) not independent; problem 7: yes, problem 6: (b) 0 (c) 1/2; (d) 1/1280; problem 8: no; problem 11: 11/36.
D&S Section 3.6: 1,3,4,5, 6,7,8,9,10,12 (Solutions: problem 4: (b) 1/3; problem 6: (b) 1/3; problem 8: (a) 0.264, (b) 0.284, (c) 0.314).
HOMEWORK 4
D&S Section 3.7: 1,2,3,5,7,8 (Solutions: problem 2: (a) 6, (b) 0.3 if (x2,x3) in {(0,0),(1,1)} and 0.2 if (x2,x3) in {(1,0),(0,1)} (c) 20x1^3(1-x1) if 0< x1< 1 and 0 o.w; problem 8: (a) 1/n!exp(-m) with m=max{y1,...,yn} for y1>0 (b) exp(-(x-m)) for x >m and 0 o.w.
D&S Section 3.8: 1,3,5,7,8,13,14 (Solutions: problem 8: 2yexp(-y^2)).
D&S Section 3.9: 1,2,3,4,6,8,12,14,15 (solutions: problem 8: n>=299;problem 12: 1-n(0.9)^{n-1}+(n-1)0.9^n; problem 14: n(n-1)y^{n-2}(1-y) for 0< y < 1 and 0 o.w.
D&S Section 3.10: 1,2,3,4,5,12 (Solutions: (a) 0.4, (b) 0.49 (c) 0.936; problem 4: (a) 0.4669, (b) 0.4662; problem 12: part (b): it is most likely that C will have the ball at time n+2).
D&S Section 3.11: 8,14,16,17,19,20,21,23 (solutions: problem 8: F(x)[1+F^2(x)-F^3(x)], 14:2/3, problem 20:2/3).
PLEASE TURN IN THE FOLLOWING PROBLEMS ON TUESDAY NOV 17: 3.7: 8; 3.8: 14; 3.9: 12, 14; 3.10: 12; 3.11: 8, 20
HOMEWORK 5
D&S Section 4.1: 3,6,7,8,11 (solutions: 6:2; 8: 1/2);
D&S Section 4.2: 3,5,7,8,9,11 (Solutions: 8: -8/5).
D&S Section 4.3: 3,4,6,7,9;
D&S Section 4.6: 5, 9, 12, 13 (Solutions: problem 12: 245/81);
D&S Section 4.4: 1, 7, 9;
D&S Section 4.7: 2, 6, 7 (Solutions: problem 2: 80.8, problem 6: 0).
D&S Section 5.3: 2, 3 (Solutions: Problem 2: 0.4266).
D&S Section 5.4: 6, 7 (Solutions: Problem 6: exp(-3.6)).
D&G Section 5.5: 2, 3 (Solutions: Problem 2: (a) 145, (b) 4350).
D&G Section 5.6: 1,2,3,4,5,11,15,16 (Solutions: problem 2(a) 0.8413 (b) 0.4013 (c) 0 (d) 0.2858 (e) 0.6915 (f) 0.2426 (g) 0.6247 (h) 0.4599; problem 4: the 25th quantile is 65.30 and the 75th is 70.698; problem 16: 0.8186).
HOMEWORK 6
Section 6.2: 5.
Section 6.3: 2,3,5,8,9,10 (Solution: problem 2: 0.0227; problem 3: 0.9938; problem 5: 542; problem 8: 0.0013, problem 9: (a) 0.36, (b) 0.7888, problem 10: (a) n>=1600 (b) n>= 106).
Please turn in the following subset of problems in class on Thursday 12/03: Section 4.1: 11; Section 4.7: 6; Section 5.6: 16; Section 6.2: 5; Section 6.3: 10.
Additional practice problems from D&S: Section 4.9: 6, 7, 8; 5.11: 2, 9, 10.