Probabilidade e Estatística UFRGS p3

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

p3/P3 - 1.pdf
p3/P3 - 2.pdf
p3/P3 - 3.pdf
p3/P3 - 4.pdf
p3/Resolu��es P3/P1 - 2.jpg
p3/Resolu��es P3/P1 - 3.jpg
p3/Resolu��es P3/P1 - 4, 5.jpg
p3/Resolu��es P3/P2 - 1, 2.jpg
p3/Resolu��es P3/P2 - 3.jpg
p3/Resolu��es P3/P3 - 1,2.jpg
p3/Resolu��es P3/P3 - 2, 3, 4.jpg
p3/src/P3 - 2/1.jpg
p3/src/P3 - 2/2.jpg
p3/src/P3 - 2/3.jpg
p3/src/P3 - 2/4.jpg
p3/src/P3 - 3/prova3a.jpg
p3/src/P3 - 3/prova3b.jpg
p3/src/P3 - 3/prova3c.jpg
p3/src/P3 - 3/prova3d.jpg
p3/src/P3 - 4.jpg
p3/Tabelas p3/tabela_normal-inversa-simplificada.pdf
 
 
 
Tabela da distribuição normal padrão inversa 
 
 
 
 
 Área ( ) 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00008 
Unilateral 4.7534 4.1075 4.0128 3.9444 3.8906 3.8461 3.7750 
Bilateral 4.8916 4.2649 4.1735 4.1075 4.0556 4.0128 3.9444 
 Área 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0008 
Unilateral 3.7190 3.5401 3.4316 3.3528 3.2910 3.2389 3.1559 
Bilateral 3.8906 3.7190 3.6153 3.5401 3.4810 3.4316 3.3528 
 Área 0.001 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 
Unilateral 3.0902 2,9677 2.8782 2,8070 2.7478 2,6968 2.6521 
Bilateral 3.2905 3,1747 3.0902 3,0233 2.9677 2,9200 2.8782 
 Área 0.0045 0.0050 0.0060 0.0070 0.0080 0.0090 0.010 
Unilateral 2,6221 2.575 2.5121 2,4573 2.4089 2,3656 2.325 
Bilateral 2,8408 2.807 2.7478 2,6968 2.6521 2,6121 2.575 
 Área 0.0150 0.020 0.0250 0.030 0.035 0.040 0.045 
Unilateral 2,1700 2.0537 1,96 1.8808 1,8119 1.7507 1,6954 
Bilateral 2,4324 2.3263 2,2414 2.1701 2,1083 2.0537 2,0046 
 Área 0.05 0.06 0.070 0.08 0.090 0.10 0.15 
Unilateral 1.645 1.5548 1,4758 1.4051 1,3407 1.2816 1.0364 
Bilateral 1.960 1.8808 1,8119 1.7507 1,6954 1.6450 1.4395 
 Área 0.20 0.25 0.30 0.35 0.40 0.45 0.50 
Unilateral 0.8416 0.6745 0.5244 0.3853 0,2533 0.1257 0 
Bilateral 1.2816 1.1503 1.0364 0.9346 0,8416 0.7554 0.6745 
 
 
 
 
p3/Tabelas p3/tabela_Qui_quadrado bilateral.pdf
 
 
 
 
 
 
 
 
 
Instruções: 
 
 
 
(1ª) A tabela fornece coordenadas para áreas bicaudais da distribuição Qui-Quadrado, isto é, 
 1)( supinf qQqP . 
 
 
 
(2ª) GL é graus de liberdade 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Áreas Bilaterais 
 GL 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.01 0.005 
1 
 
 
2 
 
 
3 
 
 
4 
 
 
5 
 
 
6 
 
 
7 
 
 
8 
 
 
9 
 
 
10 
 
 
11 
 
 
12 
 
 
13 
 
 
14 
 
 
15 
 
 
16 
 
 
17 
 
 
18 
 
 
19 
 
 
 
0.0489 0.0358 0.0247 0.0158 0.0089 0.0039 0.0010 4.E-05 1.E-05 
1.8396 2.0723 2.3535 2.7055 3.1701 3.8415 5.0239 7.8794 9.1406 
 
0.3847 0.3250 0.2671 0.2107 0.1559 0.1026 0.0506 0.0100 0.0050 
3.4859 3.7942 4.1589 4.6052 5.1805 5.9915 7.3778 10.597 11.983 
 
0.9018 0.7978 0.6924 0.5844 0.4720 0.3518 0.2158 0.0717 0.0449 
4.9566 5.317 5.7394 6.2514 6.9046 7.8147 9.3484 12.838 14.32 
 
1.5093 1.3665 1.2188 1.0636 0.8969 0.7107 0.4844 0.2070 0.1449 
6.3423 6.7449 7.214 7.7794 8.4963 9.4877 11.143 14.86 16.424 
 
2.1711 1.9938 1.8082 1.6103 1.3937 1.1455 0.8312 0.4117 0.3075 
7.6763 8.1152 8.6248 9.2364 10.008 11.07 12.833 16.75 18.386 
 
2.8698 2.6613 2.4411 2.2041 1.9415 1.6354 1.2373 0.6757 0.5266 
8.9748 9.4461 9.9917 10.645 11.466 12.592 14.449 18.548 20.249 
 
3.5956 3.3583 3.1063 2.8331 2.5277 2.1673 1.6899 0.9893 0.7945 
10.247 10.748 11.326 12.017 12.883 14.067 16.013 20.278 22.04 
 
4.3423 4.0782 3.7965 3.4895 3.144 2.7326 2.1797 1.3444 1.1043 
11.499 12.027 12.636 13.362 14.27 15.507 17.535 21.955 23.774 
 
5.1057 4.8165 4.507 4.1682 3.7847 3.3251 2.7004 1.7349 1.4501 
12.734 13.288 13.926 14.684 15.631 16.919 19.023 23.589 25.462 
 
5.8829 5.5701 5.2341 4.8652 4.4459 3.9403 3.247 2.1559 1.8274 
13.956 14.534 15.198 15.987 16.971 18.307 20.483 25.188 27.112 
 
6.6719 6.3364 5.9754 5.5778 5.1243 4.5748 3.8157 2.6032 2.2321 
15.167 15.767 16.457 17.275 18.294 19.675 21.92 26.757 28.729 
 
7.4708 7.1138 6.7288 6.3038 5.8175 5.226 4.4038 3.0738 2.6612 
16.367 16.989 17.703 18.549 19.602 21.026 23.337 28.3 30.318 
 
8.2784 7.9008 7.4929 7.0415 6.5238 5.8919 5.0088 3.565 3.1119 
17.559 18.202 18.939 19.812 20.897 22.362 24.736 29.819 31.883 
 
9.0937 8.6963 8.2662 7.7895 7.2415 6.5706 5.6287 4.0747 3.582 
18.743 19.406 20.166 21.064 22.18 23.685 26.119 31.319 33.426 
 
9.9158 9.4993 9.0479 8.5468 7.9695 7.2609 6.2621 4.6009 4.0697 
19.921 20.603 21.384 22.307 23.452 24.996 27.488 32.801 34.95 
 
10.744 10.309 9.837 9.3122 8.7067 7.9616 6.9077 5.1422 4.5734 
21.092 21.793 22.595 23.542 24.716 26.296 28.845 34.267 36.456 
 
11.578 11.125 10.633 10.085 9.4522 8.6718 7.5642 5.6972 5.0917 
22.258 22.977 23.799 24.769 25.97 27.587 30.191 35.718 37.946 
 
12.417 11.946 11.435 10.865 10.205 9.3905 8.2307 6.2648 5.6233 
23.419 24.155 24.997 25.989 27.218 28.869 31.526 37.156 39.422 
 
13.26 12.773 12.242 11.651 10.965 10.117 8.9065 6.844 6.1674 
24.575 25.329 26.189 27.204 28.458 30.144 32.852 38.582 40.885 
 
 
 
 GL 
 
 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.01 0.005 
20 
 
 
21 
 
 
22 
 
 
23 
 
 
24 
 
 
25 
 
 
26 
 
 
27 
 
 
28 
 
 
29 
 
 
30 
 
 
 31 
 
 
 32 
 
 
 33 
 
 
 34 
 
 
 35 
 
 
 36 
 
 
 37 
 
 
 38 
 
 
 39 
 
 
14.108 13.604 13.055 12.443 11.732 10.851 9.5908 7.4338 6.7228 
25.728 26.498 27.376 28.412 29.692 31.41 34.17 39.997 42.336 
 
14.959 14.439 13.873 13.24 12.504 11.591 10.283 8.0337 7.2889 
26.876 27.662 28.559 29.615 30.92 32.671 35.479 41.401 43.775 
 
15.814 15.279 14.695 14.041 13.282 12.338 10.982 8.6427 7.8649 
28.021 28.822 29.737 30.813 32.142 33.924 36.781 42.796 45.204 
 
16.673 16.122 15.521 14.848 14.065 13.091 11.689 9.2604 8.4502 
29.162 29.979 30.911 32.007 33.36 35.172 38.076 44.181 46.623 
 
17.534 16.969 16.351 15.659 14.853 13.848 12.401 9.8862 9.0442 
30.3 31.132 32.081 33.196 34.572 36.415 39.364 45.559 48.034 
 
18.399 17.818
17.184 16.473 15.645 14.611 13.12 10.52 9.6463 
31.436 32.282 33.247 34.382 35.78 37.652 40.646 46.928 49.435 
 
19.266 18.671 18.021 17.292 16.441 15.379 13.844 11.16 10.256 
32.568 33.429 34.41 35.563 36.984 38.885 41.923 48.29 50.829 
 
20.136 19.527 18.861 18.114 17.241 16.151 14.573 11.808 10.873 
33.698 34.574 35.57 36.741 38.184 40.113 43.195 49.645 52.215 
 
21.008 20.386 19.704 18.939 18.045 16.928 15.308 12.461 11.497 
34.826 35.715 36.727 37.916 39.38 41.337 44.461 50.993 53.594 
 
21.883 21.247 20.55 19.768 18.853 17.708 16.047 13.121 12.128 
35.951 36.854 37.881 39.087 40.573 42.557 45.722 52.336 54.967 
 
22.76 22.11 21.399 20.599 19.664 18.493 16.791 13.787 12.765 
37.074 37.99 39.033 40.256 41.762 43.773 46.979 53.672 56.332 
 
23.639 22.976 22.25 21.434 20.478 19.281 17.539 14.458 13.407 
38.195 39.124 40.181 41.422 42.948 44.985 48.232 55.003 57.692 
 
24.52 23.844 23.104 22.271 21.295 20.072 18.291 15.134 14.056 
39.314 40.256 41.328 42.585 44.131 46.194 49.48 56.328 59.046 
 
25.403 24.714 23.96 23.11 22.115 20.867 19.047 15.815 14.709 
40.431 41.386 42.472 43.745 45.311 47.4 50.725 57.648 60.395 
 
26.287 25.586 24.818 23.952 22.938 21.664 19.806 16.501 15.368 
41.546 42.514 43.614 44.903 46.488 48.602 51.966 58.964 61.738 
 
27.174 26.46 25.678 24.797 23.763 22.465 20.569 17.192 16.032 
42.66 43.64 44.753 46.059 47.663 49.802 53.203 60.275 63.076 
 
28.062 27.336 26.54 25.643 24.591 23.269 21.336 17.887 16.7 
43.772 44.764 45.891 47.212 48.835 50.998 54.437 61.581 64.41 
 
28.951 28.214 27.404 26.492 25.421 24.075 22.106 18.586 17.373 
44.882 45.886 47.027 48.363 50.005 52.192 55.668 62.883 65.739 
 
29.842 29.093 28.27 27.343 26.254 24.884 22.878 19.289 18.05 
45.991 47.007 48.161 49.513 51.173 53.384 56.896 64.181 67.063 
 
30.735 29.974 29.138 28.196 27.089 25.695 23.654 19.996 18.732 
47.099 48.126 49.293 50.66 52.338 54.572 58.12 65.476 68.383 
 
 
 
 
 G.L 
 
 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.01 0.005 
40 
 
 
41 
 
 
42 
 
 
43 
 
 
44 
 
 
45 
 
 
46 
 
 
47 
 
 
48 
 
 
49 
 
 
50 
 
 
51 
 
 
52 
 
 
53 
 
 
54 
 
 
55 
 
 
55 
 
 
56 
 
 
 
31.629 30.856 30.008 29.051 27.926 26.509 24.433 20.707 19.417 
48.205 49.244 50.424 51.805 53.501 55.758 59.342 66.766 69.699 
 
32.524 31.74 30.879 29.907 28.765 27.326 25.215 21.421 20.106 
49.309 50.36 51.552 52.949 54.662 56.942 60.561 68.053 71.011 
 
33.42 32.626 31.752 30.765 29.606 28.144 25.999 22.138 20.799 
50.413 51.475 52.68 54.09 55.821 58.124 61.777 69.336 72.32 
 
34.318 33.512 32.626 31.625 30.449 28.965 26.785 22.859 21.496 
51.515 52.588 53.805 55.23 56.978 59.304 62.99 70.616 73.624 
 
35.217 34.4 33.502 32.487 31.293 29.787 27.575 23.584 22.196 
52.616 53.7 54.93 56.369 58.134 60.481 64.201 71.893 74.925 
 
36.117 35.29 34.379 33.35 32.14 30.612 28.366 24.311 22.9 
53.716 54.81 56.052 57.505 59.287 61.656 65.41 73.166 76.223 
 
37.019 36.18 35.258 34.215 32.988 31.439 29.16 25.041 23.606 
54.814 55.92 57.174 58.641 60.439 62.83 66.617 74.437 77.517 
 
37.921 37.072 36.138 35.081 33.838 32.268 29.956 25.775 24.316 
55.912 57.028 58.294 59.774 61.589 64.001 67.821 75.704 78.809 
 
38.824 37.965 37.019 35.949 34.69 33.098 30.755 26.511 25.029 
57.008 58.135 59.413 60.907 62.738 65.171 69.023 76.969 80.097 
 
39.729 38.859 37.901 36.818 35.543 33.93 31.555 27.249 25.745 
58.104 59.241 60.53 62.038 63.885 66.339 70.222 78.231 81.382 
 
40.634 39.754 38.785 37.689 36.397 34.764 32.357 27.991 26.464 
59.199 60.346 61.647 63.167 65.03 67.505 71.42 79.49 82.664 
 
41.541 40.65 39.67 38.56 37.253 35.6 33.162 28.735 27.185 
60.292 61.45 62.762 64.295 66.174 68.669 72.616 80.747 83.943 
 
42.448 41.547 40.556 39.433 38.111 36.437 33.968 29.481 27.909 
61.385 62.553 63.876 65.422 67.317 69.832 73.81 82.001 85.22 
 
43.356 42.446 41.443 40.308 38.969 37.276 34.776 30.23 28.636 
62.477 63.654 64.989 66.548 68.458 70.993 75.002 83.253 86.494 
 
44.265 43.345 42.331 41.183 39.829 38.116 35.586 30.981 29.365 
63.568 64.755 66.101 67.673 69.598 72.153 76.192 84.502 87.766 
 
45.175 44.245 43.22 42.06 40.691 38.958 36.398 31.735 30.097 
64.658 65.855 67.211 68.796 70.737 73.311 77.38 85.749 89.035 
 
46.086 45.146 44.11 42.937 41.554 39.801 37.212 32.49 30.831 
65.747 66.954 68.321 69.919 71.874 74.468 78.567 86.994 90.301 
 
46.997 46.048 45.001 43.816 42.418 40.646 38.027 33.248 31.568 
66.835 68.052 69.43 71.04 73.01 75.624 79.752 88.236 91.565 
 
 
 
p3/Tabelas p3/tabela_t_student.pdf
 
 
 
 
Instruções: 
 
 
 
(1ª) GL é graus de liberdade 
 
 
(2ª) para valores unilaterias à esquerda basta trocar o sinal da coordenada, pois a 
distribuição é simétrica em torno do zero 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Coordenadas da distribuição t-student 
Áreas bilaterais 
GL 0.5 0.2 0.1 0.05 0.04 0.02 0.01 0.005 0.001 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
60 
70 
80 
90 
100 
110 
120 
1.0000 
0.8165 
0.7649 
0.7407 
0.7267 
0.7176 
0.7111 
0.7064 
0.7027 
0.6998 
0.6974 
0.6955 
0.6938 
0.6924 
0.6912 
0.6901 
0.6892 
0.6884 
0.6876 
0.6870
0.6864 
0.6858 
0.6853 
0.6848 
0.6844 
0.6840 
0.6837 
0.6834 
0.6830 
0.6828 
0.6825 
0.6822 
0.6820 
0.6818 
0.6816 
0.6814 
0.6812 
0.6810 
0.6808 
0.6807 
0.6805 
0.6804 
0.6802 
0.6801 
0.6800 
0.6799 
0.6797 
0.6796 
0.6795 
0.6794 
0.6786 
0.6780 
0.6776 
0.6772 
0.6770 
0.6767 
0.6765 
3.0777 
1.8856 
1.6377 
1.5332 
1.4759 
1.4398 
1.4149 
1.3968 
1.3830 
1.3722 
1.3634 
1.3562 
1.3502 
1.3450 
1.3406 
1.3368 
1.3334 
1.3304 
1.3277 
1.3253 
1.3232 
1.3212 
1.3195 
1.3178 
1.3163 
1.3150 
1.3137 
1.3125 
1.3114 
1.3104 
1.3095 
1.3086 
1.3077 
1.3070 
1.3062 
1.3055 
1.3049 
1.3042 
1.3036 
1.3031 
1.3025 
1.3020 
1.3016 
1.3011 
1.3006 
1.3002 
1.2998 
1.2994 
1.2991 
1.2987 
1.2958 
1.2938 
1.2922 
1.2910 
1.2901 
1.2893 
1.2886 
6.3138 
2.9200 
2.3534 
2.1318 
2.0150 
1.9432 
1.8946 
1.8595 
1.8331 
1.8125 
1.7959 
1.7823 
1.7709 
1.7613 
1.7531 
1.7459 
1.7396 
1.7341 
1.7291 
1.7247 
1.7207 
1.7171 
1.7139 
1.7109 
1.7081 
1.7056 
1.7033 
1.7011 
1.6991 
1.6973 
1.6955 
1.6939 
1.6924 
1.6909 
1.6896 
1.6883 
1.6871 
1.6860 
1.6849 
1.6839 
1.6829 
1.6820 
1.6811 
1.6802 
1.6794 
1.6787 
1.6779 
1.6772 
1.6766 
1.6759 
1.6706 
1.6669 
1.6641 
1.6620 
1.6602 
1.6588 
1.6577 
12.7062 
4.3027 
3.1824 
2.7764 
2.5706 
2.4469 
2.3646 
2.3060 
2.2622 
2.2281 
2.2010 
2.1788 
2.1604 
2.1448 
2.1314 
2.1199 
2.1098 
2.1009 
2.0930 
2.0860 
2.0796 
2.0739 
2.0687 
2.0639 
2.0595 
2.0555 
2.0518 
2.0484 
2.0452 
2.0423 
2.0395 
2.0369 
2.0345 
2.0322 
2.0301 
2.0281 
2.0262 
2.0244 
2.0227 
2.0211 
2.0195 
2.0181 
2.0167 
2.0154 
2.0141 
2.0129 
2.0117 
2.0106 
2.0096 
2.0086 
2.0003 
1.9944 
1.9901 
1.9867 
1.9840 
1.9818 
1.9799 
 
15.8945 
4.8487 
3.4819 
2.9985 
2.7565 
2.6122 
2.5168 
2.4490 
2.3984 
2.3593 
2.3281 
2.3027 
2.2816 
2.2638 
2.2485 
2.2354 
2.2238 
2.2137 
2.2047 
2.1967 
2.1894 
2.1829 
2.1770 
2.1715 
2.1666 
2.1620 
2.1578 
2.1539 
2.1503 
2.1470 
2.1438 
2.1409 
2.1382 
2.1356 
2.1332 
2.1309 
2.1287 
2.1267 
2.1247 
2.1229 
2.1212 
2.1195 
2.1179 
2.1164 
2.1150 
2.1136 
2.1123 
2.1111 
2.1099 
2.1087 
2.0994 
2.0927 
2.0878 
2.0839 
2.0809 
2.0784 
2.0763 
 
31.8205 
6.9646 
4.5407 
3.7469 
3.3649 
3.1427 
2.9980 
2.8965 
2.8214 
2.7638 
2.7181 
2.6810 
2.6503 
2.6245 
2.6025 
2.5835 
2.5669 
2.5524 
2.5395 
2.5280 
2.5176 
2.5083 
2.4999 
2.4922 
2.4851 
2.4786 
2.4727 
2.4671 
2.4620 
2.4573 
2.4528 
2.4487 
2.4448 
2.4411 
2.4377 
2.4345 
2.4314 
2.4286 
2.4258 
2.4233 
2.4208 
2.4185 
2.4163 
2.4141 
2.4121 
2.4102 
2.4083 
2.4066 
2.4049 
2.4033 
2.3901 
2.3808 
2.3739 
2.3685 
2.3642 
2.3607 
2.3578 
 
63.6567 
9.9248 
5.8409 
4.6041 
4.0321 
3.7074 
3.4995 
3.3554 
3.2498 
3.1693 
3.1058 
3.0545 
3.0123 
2.9768 
2.9467 
2.9208 
2.8982 
2.8784 
2.8609 
2.8453 
2.8314 
2.8188 
2.8073 
2.7969 
2.7874 
2.7787 
2.7707 
2.7633 
2.7564 
2.7500 
2.7440 
2.7385 
2.7333 
2.7284 
2.7238 
2.7195 
2.7154 
2.7116 
2.7079 
2.7045 
2.7012 
2.6981 
2.6951 
2.6923 
2.6896 
2.6870 
2.6846 
2.6822 
2.6800 
2.6778 
2.6603 
2.6479 
2.6387 
2.6316 
2.6259 
2.6213 
2.6174 
 
127.3213 
14.0890 
7.4533 
5.5976 
4.7733 
4.3168 
4.0293 
3.8325 
3.6897 
3.5814 
3.4966 
3.4284 
3.3725 
3.3257 
3.2860 
3.2520 
3.2224 
3.1966 
3.1737 
3.1534 
3.1352 
3.1188 
3.1040 
3.0905 
3.0782 
3.0669 
3.0565 
3.0469 
3.0380 
3.0298 
3.0221 
3.0149 
3.0082 
3.0020 
2.9960 
2.9905 
2.9852 
2.9803 
2.9756 
2.9712 
2.9670 
2.9630 
2.9592 
2.9555 
2.9521 
2.9488 
2.9456 
2.9426 
2.9397 
2.9370 
2.9146 
2.8987 
2.8870 
2.8779 
2.8707 
2.8648 
2.8599 
 
636.6192 
31.5991 
12.9240 
8.6103 
6.8688 
5.9588 
5.4079 
5.0413 
4.7809 
4.5869 
4.4370 
4.3178 
4.2208 
4.1405 
4.0728 
4.0150 
3.9651 
3.9216 
3.8834 
3.8495 
3.8193 
3.7921 
3.7676 
3.7454 
3.7251 
3.7066 
3.6896 
3.6739 
3.6594 
3.6460 
3.6335 
3.6218 
3.6109 
3.6007 
3.5911 
3.5821 
3.5737 
3.5657 
3.5581 
3.5510 
3.5442 
3.5377 
3.5316 
3.5258 
3.5203 
3.5150 
3.5099 
3.5051 
3.5004 
3.4960 
3.4602 
3.4350 
3.4163 
3.4019 
3.3905 
3.3812 
3.3735 
 
>120 0.674 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.290 
 0,25 0,10 0,05 0,025 0,02 0,01 0,005 0,0025 0,0005 
 Áreas unilaterais