Таблица Лапласа
Если вы студент и изучаете курс теории вероятностей или математическую статистику, то вам точно пригодятся эта таблица при решении задач. Значения функции Лапласа - вероятность того, что случайная величина примет значение,
принадлежащее заданному интервалу. Используют таблицу так: по известному значению аргумента функции надо найти ее значение или, наоборот, по известному значению функции Лапласа требуется найти значение аргумента. Это функция нормального распределения.
Функция Лапласа
$$F\left(t \right)=\frac{2}{\sqrt{2\pi }}\int_{0}^{t}{e^{-t^{2}/2}dt}$$
Функция нечетная , поэтому по таблице можно вычислять и значения от отрицательного аргумента по формуле:.
$$F\left(-t \right)=-F\left(t \right)$$
Таблица значений функции Лапласа
| t |
F(t) |
| 0.00 |
0.00000 |
| 0.01 |
0.00798 |
| 0.02 |
0.01596 |
| 0.03 |
0.02393 |
| 0.04 |
0.03191 |
| 0.05 |
0.03988 |
| 0.06 |
0.04784 |
| 0.07 |
0.05581 |
| 0.08 |
0.06376 |
| 0.09 |
0.07171 |
| 0.10 |
0.07966 |
| 0.11 |
0.08759 |
| 0.12 |
0.09552 |
| 0.13 |
0.10348 |
| 0.14 |
0.11134 |
| 0.15 |
0.11924 |
| 0.16 |
0.12712 |
| 0.17 |
0.13499 |
| 0.18 |
0.14285 |
| 0.19 |
0.15069 |
| 0.20 |
0.15852 |
| 0.21 |
0.16633 |
| 0.22 |
0.17413 |
| 0.23 |
0.18191 |
| 0.24 |
0.18967 |
| 0.25 |
0.19741 |
| 0.26 |
0.20514 |
| 0.27 |
0.21284 |
| 0.28 |
0.22052 |
| 0.29 |
0.22818 |
| 0.30 |
0.23582 |
| 0.31 |
0.24344 |
| 0.32 |
0.25103 |
| 0.33 |
0.25860 |
| 0.34 |
0.26614 |
| 0.35 |
0.27366 |
| 0.36 |
0.28115 |
| 0.37 |
0.28862 |
| 0.38 |
0.29605 |
| 0.39 |
0.30346 |
| 0.40 |
0.31084 |
| 0.41 |
0.31819 |
| 0.42 |
0.32552 |
| 0.43 |
0.33280 |
| 0.44 |
0.34006 |
| 0.45 |
0.34729 |
| 0.46 |
0.35448 |
| 0.47 |
0.36164 |
| 0.48 |
0.36877 |
| 0.49 |
0.37587 |
| 0.50 |
0.38292 |
| 0.51 |
0.38995 |
| 0.52 |
0.39694 |
| 0.53 |
0.40389 |
| 0.54 |
0.41080 |
| 0.55 |
0.41768 |
| 0.56 |
0.42452 |
| 0.57 |
0.43132 |
| 0.58 |
0.43809 |
| 0.59 |
0.44481 |
| 0.60 |
0.45149 |
| 0.61 |
0.45814 |
| 0.62 |
0.46474 |
| 0.63 |
0.47131 |
| 0.64 |
0.47783 |
| 0.65 |
0.48431 |
| 0.66 |
0.49075 |
| 0.67 |
0.49714 |
| 0.68 |
0.50350 |
| 0.69 |
0.50981 |
| 0.70 |
0.51607 |
| 0.71 |
0.52230 |
| 0.72 |
0.52848 |
| 0.73 |
0.53461 |
| 0.74 |
0.54070 |
| 0.75 |
0.54675 |
| 0.76 |
0.55275 |
| 0.77 |
0.55870 |
| 0.78 |
0.56461 |
| 0.79 |
0.57047 |
| 0.80 |
0.57629 |
| 0.81 |
0.58206 |
| 0.82 |
0.58778 |
| 0.83 |
0.59346 |
| 0.84 |
0.59909 |
| 0.85 |
0.60468 |
| 0.86 |
0.61021 |
| 0.87 |
0.61570 |
| 0.88 |
0.62114 |
| 0.89 |
0.62653 |
| 0.90 |
0.63188 |
| 0.91 |
0.63718 |
| 0.92 |
0.64243 |
| 0.93 |
0.64763 |
| 0.94 |
0.65278 |
| 0.95 |
0.65789 |
| 0.96 |
0.66294 |
| 0.97 |
0.66795 |
| 0.98 |
0.67291 |
| 0.99 |
0.67783 |
|
| t |
F(t) |
| 1.00 |
0.68269 |
| 1.01 |
0.68750 |
| 1.02 |
0.69227 |
| 1.03 |
0.69699 |
| 1.04 |
0.70166 |
| 1.05 |
0.70628 |
| 1.06 |
0.71086 |
| 1.07 |
0.71538 |
| 1.08 |
0.71986 |
| 1.09 |
0.72429 |
| 1.10 |
0.72867 |
| 1.11 |
0.73300 |
| 1.12 |
0.73729 |
| 1.13 |
0.74152 |
| 1.14 |
0.74571 |
| 1.15 |
0.74986 |
| 1.16 |
0.75395 |
| 1.17 |
0.75800 |
| 1.18 |
0.76200 |
| 1.19 |
0.76595 |
| 1.20 |
0.76986 |
| 1.21 |
0.77372 |
| 1.22 |
0.77754 |
| 1.23 |
0.78130 |
| 1.24 |
0.78502 |
| 1.25 |
0.78870 |
| 1.26 |
0.79233 |
| 1.27 |
0.79592 |
| 1.28 |
0.79945 |
| 1.29 |
0.80295 |
| 1.30 |
0.80640 |
| 1.31 |
0.80980 |
| 1.32 |
0.81316 |
| 1.33 |
0.81648 |
| 1.34 |
0.81975 |
| 1.35 |
0.82298 |
| 1.36 |
0.82617 |
| 1.37 |
0.82931 |
| 1.38 |
0.83241 |
| 1.39 |
0.83547 |
| 1.40 |
0.83849 |
| 1.41 |
0.84146 |
| 1.42 |
0.84439 |
| 1.43 |
0.84728 |
| 1.44 |
0.85013 |
| 1.45 |
0.85294 |
| 1.46 |
0.85571 |
| 1.47 |
0.85844 |
| 1.48 |
0.86113 |
| 1.49 |
0.86378 |
| 1.50 |
0.86639 |
| 1.51 |
0.86696 |
| 1.52 |
0.87149 |
| 1.53 |
0.87398 |
| 1.54 |
0.87644 |
| 1.55 |
0.87886 |
| 1.56 |
0.88124 |
| 1.57 |
0.88358 |
| 1.58 |
0.88589 |
| 1.59 |
0.88817 |
| 1.60 |
0.89040 |
| 1.61 |
0.89260 |
| 1.62 |
0.89477 |
| 1.63 |
0.89690 |
| 1.64 |
0.89899 |
| 1.65 |
0.90106 |
| 1.66 |
0.90309 |
| 1.67 |
0.90508 |
| 1.68 |
0.90704 |
| 1.69 |
0.90897 |
| 1.70 |
0.91087 |
| 1.71 |
0.91273 |
| 1.72 |
0.91457 |
| 1.73 |
0.91637 |
| 1.74 |
0.91814 |
| 1.75 |
0.91988 |
| 1.76 |
0.92159 |
| 1.77 |
0.92327 |
| 1.78 |
0.92492 |
| 1.79 |
0.92655 |
| 1.80 |
0.92814 |
| 1.81 |
0.92970 |
| 1.82 |
0.93124 |
| 1.83 |
0.93275 |
| 1.84 |
0.93423 |
| 1.85 |
0.93569 |
| 1.86 |
0.93711 |
| 1.87 |
0.93852 |
| 1.88 |
0.93989 |
| 1.89 |
0.94124 |
| 1.90 |
0.94257 |
| 1.91 |
0.94387 |
| 1.92 |
0.94514 |
| 1.93 |
0.94639 |
| 1.94 |
0.94762 |
| 1.95 |
0.94882 |
| 1.96 |
0.95000 |
| 1.97 |
0.95116 |
| 1.98 |
0.95230 |
| 1.99 |
0.95341 |
|
| t |
F(t) |
| 2.00 |
0.95450 |
| 2.01 |
0.95557 |
| 2.02 |
0.95662 |
| 2.03 |
0.95764 |
| 2.04 |
0.95865 |
| 2.05 |
0.95964 |
| 2.06 |
0.96060 |
| 2.07 |
0.96155 |
| 2.08 |
0.96247 |
| 2.09 |
0.96338 |
| 2.10 |
0.96427 |
| 2.11 |
0.96514 |
| 2.12 |
0.96599 |
| 2.13 |
0.96683 |
| 2.14 |
0.96765 |
| 2.15 |
0.96844 |
| 2.16 |
0.96923 |
| 2.17 |
0.96999 |
| 2.18 |
0.97074 |
| 2.19 |
0.97148 |
| 2.20 |
0.97219 |
| 2.21 |
0.97289 |
| 2.22 |
0.97358 |
| 2.23 |
0.97425 |
| 2.24 |
0.97491 |
| 2.25 |
0.97555 |
| 2.26 |
0.97618 |
| 2.27 |
0.97679 |
| 2.28 |
0.97739 |
| 2.29 |
0.97798 |
| 2.30 |
0.97855 |
| 2.31 |
0.97911 |
| 2.32 |
0.97966 |
| 2.33 |
0.98019 |
| 2.34 |
0.98072 |
| 2.35 |
0.98123 |
| 2.36 |
0.98172 |
| 2.37 |
0.98221 |
| 2.38 |
0.98269 |
| 2.39 |
0.98315 |
| 2.40 |
0.98360 |
| 2.41 |
0.98405 |
| 2.42 |
0.98448 |
| 2.43 |
0.98490 |
| 2.44 |
0.98531 |
| 2.45 |
0.98571 |
| 2.46 |
0.98611 |
| 2.47 |
0.98649 |
| 2.48 |
0.98686 |
| 2.49 |
0.98723 |
| 2.50 |
0.98758 |
| 2.51 |
0.98793 |
| 2.52 |
0.98826 |
| 2.53 |
0.98859 |
| 2.54 |
0.98891 |
| 2.55 |
0.98923 |
| 2.56 |
0.98953 |
| 2.57 |
0.98983 |
| 2.58 |
0.99012 |
| 2.59 |
0.99040 |
| 2.60 |
0.99068 |
| 2.61 |
0.99095 |
| 2.62 |
0.99121 |
| 2.63 |
0.99146 |
| 2.64 |
0.99171 |
| 2.65 |
0.99195 |
| 2.66 |
0.99219 |
| 2.67 |
0.99241 |
| 2.68 |
0.99263 |
| 2.69 |
0.99285 |
| 2.70 |
0.99307 |
| 2.71 |
0.99327 |
| 2.72 |
0.99347 |
| 2.73 |
0.99367 |
| 2.74 |
0.99386 |
| 2.75 |
0.99404 |
| 2.76 |
0.99422 |
| 2.77 |
0.99439 |
| 2.78 |
0.99456 |
| 2.79 |
0.99473 |
| 2.80 |
0.99489 |
| 2.81 |
0.99505 |
| 2.82 |
0.99520 |
| 2.83 |
0.99535 |
| 2.84 |
0.99549 |
| 2.85 |
0.99563 |
| 2.86 |
0.99576 |
| 2.87 |
0.99590 |
| 2.88 |
0.99602 |
| 2.89 |
0.99615 |
| 2.90 |
0.99627 |
| 2.91 |
0.99639 |
| 2.92 |
0.99650 |
| 2.93 |
0.99661 |
| 2.94 |
0.99672 |
| 2.95 |
0.99682 |
| 2.96 |
0.99692 |
| 2.97 |
0.99702 |
| 2.98 |
0.99712 |
| 2.99 |
0.99721 |
|
| t |
F(t) |
| 3.00 |
0.99730 |
| 3.01 |
0.99739 |
| 3.02 |
0.99747 |
| 3.03 |
0.99755 |
| 3.04 |
0.99763 |
| 3.05 |
0.99771 |
| 3.06 |
0.99779 |
| 3.07 |
0.99786 |
| 3.08 |
0.99793 |
| 3.09 |
0.99800 |
| 3.10 |
0.99806 |
| 3.11 |
0.99813 |
| 3.12 |
0.99819 |
| 3.13 |
0.99825 |
| 3.14 |
0.99831 |
| 3.15 |
0.99837 |
| 3.16 |
0.99842 |
| 3.17 |
0.99848 |
| 3.18 |
0.99853 |
| 3.19 |
0.99858 |
| 3.20 |
0.99863 |
| 3.21 |
0.99867 |
| 3.22 |
0.99872 |
| 3.23 |
0.99876 |
| 3.24 |
0.99880 |
| 3.25 |
0.99855 |
| 3.26 |
0.99889 |
| 3.27 |
0.99892 |
| 3.28 |
0.99896 |
| 3.29 |
0.99900 |
| 3.30 |
0.99903 |
| 3.31 |
0.99907 |
| 3.32 |
0.99910 |
| 3.33 |
0.99913 |
| 3.34 |
0.99916 |
| 3.35 |
0.99919 |
| 3.36 |
0.99922 |
| 3.37 |
0.99925 |
| 3.38 |
0.99928 |
| 3.39 |
0.99930 |
| 3.40 |
0.99933 |
| 3.41 |
0.99935 |
| 3.42 |
0.99937 |
| 3.43 |
0.99940 |
| 3.44 |
0.99942 |
| 3.45 |
0.99944 |
| 3.46 |
0.99946 |
| 3.47 |
0.99948 |
| 3.48 |
0.99950 |
| 3.49 |
0.99952 |
| 3.50 |
0.99953 |
| 3.51 |
0.99955 |
| 3.52 |
0.99957 |
| 3.53 |
0.99958 |
| 3.54 |
0.99960 |
| 3.55 |
0.99961 |
| 3.56 |
0.99963 |
| 3.57 |
0.99964 |
| 3.58 |
0.99966 |
| 3.59 |
0.99967 |
| 3.60 |
0.99968 |
| 3.61 |
0.99969 |
| 3.62 |
0.99971 |
| 3.63 |
0.99972 |
| 3.64 |
0.99973 |
| 3.65 |
0.99974 |
| 3.66 |
0.99975 |
| 3.67 |
0.99976 |
| 3.68 |
0.99977 |
| 3.69 |
0.99978 |
| 3.70 |
0.99978 |
| 3.71 |
0.99979 |
| 3.72 |
0.99980 |
| 3.73 |
0.99981 |
| 3.74 |
0.99982 |
| 3.75 |
0.99982 |
| 3.76 |
0.99983 |
| 3.77 |
0.99984 |
| 3.78 |
0.99984 |
| 3.79 |
0.99985 |
| 3.80 |
0.99986 |
| 3.81 |
0.99986 |
| 3.82 |
0.99987 |
| 3.83 |
0.99987 |
| 3.84 |
0.99988 |
| 3.85 |
0.99988 |
| 3.86 |
0.99989 |
| 3.87 |
0.99989 |
| 3.88 |
0.99990 |
| 3.89 |
0.99990 |
| 3.90 |
0.99990 |
| 3.91 |
0.99991 |
| 3.92 |
0.99991 |
| 3.93 |
0.99992 |
| 3.94 |
0.99992 |
| 3.95 |
0.99992 |
| 3.96 |
0.99992 |
| 3.97 |
0.99993 |
| 3.98 |
0.99993 |
| 3.99 |
0.99993 |
|
