Homework

HOMEWORK 1

D&S Section 1.4: 5, 7, 8; 

D&S 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); 

D&S Section 1.6: 4, 5, 6 (solutions: problem 4: 1/7; problem 6: 1/4); 

D&S 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). 

D&S Section 1.9: 3, 5, 8 (solutions: problem 8: 0.0324). 

D&S Section 1.10: 7, 8, 10, 12, 13 (Solutions: problem 10:0.5).

PLEASE TURN IN THE FOLLOWING PROBLEMS (DUE: OCT-13 (F)):  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); 

D&S 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;

D&S Section 2.3: 4, 5, 6, 7 (problem 4: approx 0.00019, problem 6: (a) 96/97 (b) 64/65).

Kadane Section 2.3.2: problems 2 and 3.

Kadane Section 2.4.2: problems 3 and 6.

PLEASE TURN IN THE FOLLOWING PROBLEMS (DUE: OCT-20 (F)):  D&S Section 2.1: 12; Section 2:2: 16, 22, 23. Section 2.3: 5. Kadane Section 2.3.2: problem 2.

 

HOMEWORK 3

D&S Section 3.1: 2, 5, 6, 7, 8, 10, 11 (Problem 2: 1/15, problem 6: 0.1509, problem 8: 0.1330, problem 10: (b) 1/3).

D&S 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). 

D&S 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). 

 PLEASE TURN IN THE FOLLOWING PROBLEMS (DUE: Nov-01 (W) -- changed! ):  D&S Section 3.1: 10, 11; Section 3.2: 8. Section 3.3: 4, Section 3.4: 8, Section 3.5: 4, Section 3.6: 7.

 

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 (Due: NOV-15 (W) ):  D&S 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 4.4: 1, 7, 9; 

D&S Section 4.6: 5, 9, 12, 13 (Solutions: problem 12: 245/81); 

D&S Section 4.7: 2, 6, 7 (Solutions: problem 2: 80.8, problem 6: 0). 

Additional practice problems from D&S: Section 4.9: 6, 7, 8;

PLEASE TURN IN THE FOLLOWING PROBLEMS (Due: NOV-29 (W) ):  4.1: 11; 4.2: 7; 4.6: 9; 4.7: 7;

 

HOMEWORK 6

D&S Section 5.2: 8 (0.6993).

D&S Section 5.3: 2, 3 (Solutions: Problem 2: 0.4266). 

D&S Section 5.4: 3, 6, 7 (Solutions: Problem 6: exp(-3.6)). 

D&S Section 5.5: 1, 2, 3 (Solutions: Problem 2: (a) 145, (b) 4350).   

D&S 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).

Additional practice problems from D&S:  5.11:  2, 9, 10.

D&S Section 6.2: 5. 

D&S 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 PROBLEMS (Due: DEC-8 (F) ):  5.3: 2; 5.4: 7; 5.6: 5, 15;  6.3: 9, 10.