From c1e60a0cd381ed74aec83077c23a0a16f66f72da Mon Sep 17 00:00:00 2001 From: Daniel Thiem Date: Wed, 26 Sep 2012 10:59:38 +0200 Subject: [PATCH] Mengenlehere --- document.pdf | 7556 +++++++++++++++++++++++++------------------------- document.tex | 18 +- 2 files changed, 3831 insertions(+), 3743 deletions(-) diff --git a/document.pdf b/document.pdf index 8ea5a65..55ddc8b 100644 --- a/document.pdf +++ b/document.pdf @@ -10,670 +10,679 @@ endobj << /S /GoTo /D (section.1.1) >> endobj 8 0 obj -(Wahrscheinlichkeitsdichtefunktion) +(Megenlehre) endobj 9 0 obj -<< /S /GoTo /D (subsection.1.1.1) >> -endobj -12 0 obj -(Eigenschaften der Wahrscheinlichkeitsdichtefunktion) -endobj -13 0 obj -<< /S /GoTo /D (subsection.1.1.2) >> -endobj -16 0 obj -(Berechnung bei Abhngigkeit zu anderer Zufallsvariablen) -endobj -17 0 obj << /S /GoTo /D (section.1.2) >> endobj -20 0 obj -(Verteilungsfunktion) +12 0 obj +(Wahrscheinlichkeitsdichtefunktion) endobj -21 0 obj +13 0 obj << /S /GoTo /D (subsection.1.2.1) 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>> endobj 79 0 obj << /Title 80 0 R /A 77 0 R -/Parent 75 0 R -/Next 83 0 R +/Parent 3 0 R +/Prev 67 0 R +/First 83 0 R +/Last 99 0 R +/Count -5 >> endobj 75 0 obj << /Title 76 0 R /A 73 0 R -/Parent 3 0 R -/Prev 63 0 R -/First 79 0 R -/Last 95 0 R -/Count -5 +/Parent 67 0 R +/Prev 71 0 R >> endobj 71 0 obj << /Title 72 0 R /A 69 0 R -/Parent 63 0 R -/Prev 67 0 R +/Parent 67 0 R +/Next 75 0 R >> endobj 67 0 obj << /Title 68 0 R /A 65 0 R -/Parent 63 0 R -/Next 71 0 R +/Parent 3 0 R +/Prev 55 0 R +/Next 79 0 R +/First 71 0 R +/Last 75 0 R +/Count -2 >> endobj 63 0 obj << /Title 64 0 R /A 61 0 R -/Parent 3 0 R -/Prev 51 0 R -/Next 75 0 R -/First 67 0 R -/Last 71 0 R -/Count -2 +/Parent 55 0 R +/Prev 59 0 R >> endobj 59 0 obj << /Title 60 0 R /A 57 0 R -/Parent 51 0 R -/Prev 55 0 R +/Parent 55 0 R +/Next 63 0 R >> endobj 55 0 obj << /Title 56 0 R /A 53 0 R -/Parent 51 0 R -/Next 59 0 R +/Parent 3 0 R +/Prev 51 0 R +/Next 67 0 R +/First 59 0 R +/Last 63 0 R +/Count -2 >> endobj 51 0 obj << /Title 52 0 R /A 49 0 R /Parent 3 0 R -/Prev 47 0 R -/Next 63 0 R -/First 55 0 R -/Last 59 0 R -/Count -2 +/Prev 35 0 R +/Next 55 0 R >> endobj 47 0 obj << /Title 48 0 R /A 45 0 R -/Parent 3 0 R -/Prev 31 0 R -/Next 51 0 R +/Parent 35 0 R +/Prev 43 0 R >> endobj 43 0 obj << /Title 44 0 R /A 41 0 R -/Parent 31 0 R +/Parent 35 0 R /Prev 39 0 R +/Next 47 0 R >> endobj 39 0 obj << /Title 40 0 R /A 37 0 R -/Parent 31 0 R -/Prev 35 0 R +/Parent 35 0 R /Next 43 0 R >> endobj 35 0 obj << /Title 36 0 R /A 33 0 R -/Parent 31 0 R -/Next 39 0 R +/Parent 3 0 R +/Prev 23 0 R +/Next 51 0 R +/First 39 0 R +/Last 47 0 R +/Count -3 >> endobj 31 0 obj << /Title 32 0 R /A 29 0 R -/Parent 3 0 R -/Prev 19 0 R -/Next 47 0 R -/First 35 0 R -/Last 43 0 R -/Count -3 +/Parent 23 0 R +/Prev 27 0 R >> endobj 27 0 obj << /Title 28 0 R /A 25 0 R -/Parent 19 0 R -/Prev 23 0 R +/Parent 23 0 R +/Next 31 0 R >> endobj 23 0 obj << /Title 24 0 R /A 21 0 R -/Parent 19 0 R -/Next 27 0 R +/Parent 3 0 R +/Prev 11 0 R +/Next 35 0 R +/First 27 0 R +/Last 31 0 R +/Count -2 >> endobj 19 0 obj << /Title 20 0 R /A 17 0 R -/Parent 3 0 R -/Prev 7 0 R -/Next 31 0 R -/First 23 0 R -/Last 27 0 R -/Count -2 +/Parent 11 0 R +/Prev 15 0 R >> endobj 15 0 obj << /Title 16 0 R /A 13 0 R -/Parent 7 0 R -/Prev 11 0 R +/Parent 11 0 R +/Next 19 0 R >> endobj 11 0 obj << /Title 12 0 R /A 9 0 R -/Parent 7 0 R -/Next 15 0 R +/Parent 3 0 R +/Prev 7 0 R +/Next 23 0 R +/First 15 0 R +/Last 19 0 R +/Count -2 >> endobj 7 0 obj << /Title 8 0 R /A 5 0 R /Parent 3 0 R -/Next 19 0 R -/First 11 0 R -/Last 15 0 R -/Count -2 +/Next 11 0 R >> endobj 3 0 obj << /Title 4 0 R /A 1 0 R -/Parent 973 0 R -/Next 99 0 R +/Parent 990 0 R +/Next 103 0 R /First 7 0 R -/Last 75 0 R -/Count -7 ->> endobj -974 0 obj << -/Names [(Doc-Start) 441 0 R (Item.1) 673 0 R (Item.2) 674 0 R (Item.3) 812 0 R (Item.4) 813 0 R (Item.5) 814 0 R] -/Limits [(Doc-Start) (Item.5)] ->> endobj -975 0 obj << -/Names [(chapter*.1) 489 0 R (chapter.1) 2 0 R (chapter.2) 98 0 R (chapter.3) 142 0 R (chapter.4) 238 0 R (chapter.5) 306 0 R] -/Limits [(chapter*.1) (chapter.5)] ->> endobj -976 0 obj << -/Names [(chapter.6) 394 0 R (equation.1.1) 591 0 R (equation.1.10) 625 0 R (equation.1.11) 626 0 R (equation.1.12) 627 0 R (equation.1.13) 629 0 R] -/Limits [(chapter.6) (equation.1.13)] ->> endobj -977 0 obj << -/Names [(equation.1.14) 635 0 R (equation.1.15) 636 0 R (equation.1.16) 637 0 R (equation.1.17) 638 0 R (equation.1.18) 639 0 R (equation.1.19) 640 0 R] -/Limits [(equation.1.14) (equation.1.19)] ->> endobj -978 0 obj << -/Names [(equation.1.2) 592 0 R (equation.1.20) 641 0 R (equation.1.21) 654 0 R (equation.1.22) 655 0 R (equation.1.23) 656 0 R (equation.1.24) 657 0 R] -/Limits [(equation.1.2) (equation.1.24)] ->> endobj -979 0 obj << -/Names [(equation.1.2a) 595 0 R (equation.1.2b) 596 0 R (equation.1.3) 597 0 R (equation.1.4) 599 0 R (equation.1.5) 605 0 R (equation.1.5a) 606 0 R] -/Limits [(equation.1.2a) (equation.1.5a)] ->> endobj -980 0 obj << -/Names [(equation.1.5b) 607 0 R (equation.1.5c) 608 0 R (equation.1.5d) 610 0 R (equation.1.6) 611 0 R (equation.1.6a) 612 0 R (equation.1.6b) 613 0 R] -/Limits [(equation.1.5b) (equation.1.6b)] ->> endobj -981 0 obj << -/Names [(equation.1.6c) 614 0 R (equation.1.6d) 615 0 R (equation.1.6e) 616 0 R (equation.1.6f) 617 0 R (equation.1.7) 618 0 R (equation.1.8) 623 0 R] -/Limits [(equation.1.6c) (equation.1.8)] ->> endobj -982 0 obj << -/Names [(equation.1.9) 624 0 R (equation.2.1) 662 0 R (equation.2.2) 663 0 R (equation.2.3) 664 0 R (equation.2.4) 665 0 R (equation.2.5) 671 0 R] -/Limits [(equation.1.9) (equation.2.5)] ->> endobj -983 0 obj << -/Names [(equation.2.6) 672 0 R (equation.2.7) 675 0 R (equation.2.7a) 677 0 R (equation.2.7b) 678 0 R (equation.3.1) 685 0 R (equation.3.10) 708 0 R] -/Limits [(equation.2.6) (equation.3.10)] ->> endobj -984 0 obj << -/Names [(equation.3.10a) 709 0 R (equation.3.10b) 710 0 R (equation.3.11) 716 0 R (equation.3.12) 717 0 R (equation.3.12a) 718 0 R (equation.3.12b) 719 0 R] -/Limits [(equation.3.10a) (equation.3.12b)] ->> endobj -985 0 obj << -/Names [(equation.3.13) 720 0 R (equation.3.14) 721 0 R (equation.3.14a) 722 0 R (equation.3.14b) 723 0 R (equation.3.15) 724 0 R (equation.3.16) 730 0 R] -/Limits [(equation.3.13) (equation.3.16)] ->> endobj -986 0 obj << -/Names [(equation.3.17) 731 0 R (equation.3.18) 732 0 R (equation.3.19) 733 0 R (equation.3.2) 686 0 R (equation.3.20) 735 0 R (equation.3.21) 736 0 R] -/Limits [(equation.3.17) (equation.3.21)] ->> endobj -987 0 obj << -/Names [(equation.3.22) 743 0 R (equation.3.23) 744 0 R (equation.3.3) 687 0 R (equation.3.3a) 688 0 R (equation.3.3b) 689 0 R (equation.3.4) 690 0 R] -/Limits [(equation.3.22) (equation.3.4)] ->> endobj -988 0 obj << -/Names [(equation.3.4a) 691 0 R (equation.3.4b) 692 0 R (equation.3.4c) 693 0 R (equation.3.5) 694 0 R (equation.3.6) 701 0 R (equation.3.7) 702 0 R] -/Limits [(equation.3.4a) (equation.3.7)] ->> endobj -989 0 obj << -/Names [(equation.3.7a) 703 0 R (equation.3.7b) 704 0 R (equation.3.7c) 705 0 R (equation.3.8) 706 0 R (equation.3.9) 707 0 R (equation.4.1) 749 0 R] -/Limits [(equation.3.7a) (equation.4.1)] ->> endobj -990 0 obj << -/Names [(equation.4.10) 794 0 R (equation.4.11) 795 0 R (equation.4.12) 802 0 R (equation.4.13) 803 0 R (equation.4.14) 804 0 R (equation.4.15) 805 0 R] -/Limits [(equation.4.10) (equation.4.15)] +/Last 79 0 R +/Count -8 >> endobj 991 0 obj << -/Names [(equation.4.16) 815 0 R (equation.4.17) 816 0 R (equation.4.18) 818 0 R (equation.4.18a) 819 0 R (equation.4.18b) 820 0 R (equation.4.18c) 821 0 R] -/Limits [(equation.4.16) (equation.4.18c)] +/Names [(Doc-Start) 445 0 R (Item.1) 691 0 R (Item.2) 692 0 R (Item.3) 829 0 R (Item.4) 830 0 R (Item.5) 831 0 R] +/Limits [(Doc-Start) (Item.5)] >> endobj 992 0 obj << -/Names [(equation.4.18d) 822 0 R (equation.4.2) 750 0 R (equation.4.3) 752 0 R (equation.4.3a) 754 0 R (equation.4.3b) 755 0 R (equation.4.3c) 756 0 R] -/Limits [(equation.4.18d) (equation.4.3c)] +/Names [(chapter*.1) 493 0 R (chapter.1) 2 0 R (chapter.2) 102 0 R (chapter.3) 146 0 R (chapter.4) 242 0 R (chapter.5) 310 0 R] +/Limits [(chapter*.1) (chapter.5)] >> endobj 993 0 obj << -/Names [(equation.4.4) 773 0 R (equation.4.4a) 774 0 R (equation.4.4b) 775 0 R (equation.4.5) 776 0 R (equation.4.6) 778 0 R (equation.4.6a) 779 0 R] -/Limits [(equation.4.4) (equation.4.6a)] +/Names [(chapter.6) 398 0 R (equation.1.1) 596 0 R (equation.1.10) 636 0 R (equation.1.11) 637 0 R (equation.1.12) 638 0 R (equation.1.13) 639 0 R] +/Limits [(chapter.6) (equation.1.13)] >> endobj 994 0 obj << -/Names [(equation.4.6b) 780 0 R (equation.4.6c) 782 0 R (equation.4.6d) 783 0 R (equation.4.6e) 784 0 R (equation.4.7) 785 0 R (equation.4.8) 790 0 R] -/Limits [(equation.4.6b) (equation.4.8)] +/Names [(equation.1.14) 640 0 R (equation.1.15) 646 0 R (equation.1.16) 648 0 R (equation.1.17) 649 0 R (equation.1.18) 650 0 R (equation.1.19) 651 0 R] +/Limits [(equation.1.14) (equation.1.19)] >> endobj 995 0 obj << -/Names [(equation.4.8a) 791 0 R (equation.4.8b) 792 0 R (equation.4.9) 793 0 R (equation.5.1) 836 0 R (equation.5.10) 865 0 R (equation.5.11) 872 0 R] -/Limits [(equation.4.8a) (equation.5.11)] +/Names [(equation.1.1a) 598 0 R (equation.1.1b) 599 0 R (equation.1.1c) 600 0 R (equation.1.1d) 601 0 R (equation.1.1e) 603 0 R (equation.1.1f) 605 0 R] +/Limits [(equation.1.1a) (equation.1.1f)] >> endobj 996 0 obj << -/Names [(equation.5.12) 873 0 R (equation.5.13) 874 0 R (equation.5.14) 882 0 R (equation.5.14a) 883 0 R (equation.5.14b) 884 0 R (equation.5.15) 885 0 R] -/Limits [(equation.5.12) (equation.5.15)] +/Names [(equation.1.2) 606 0 R (equation.1.20) 656 0 R (equation.1.21) 657 0 R (equation.1.22) 658 0 R (equation.1.23) 659 0 R (equation.1.24) 660 0 R] +/Limits [(equation.1.2) (equation.1.24)] >> endobj 997 0 obj << -/Names [(equation.5.16) 890 0 R (equation.5.17) 891 0 R (equation.5.18) 892 0 R (equation.5.18a) 893 0 R (equation.5.18b) 894 0 R (equation.5.19) 895 0 R] -/Limits [(equation.5.16) (equation.5.19)] +/Names [(equation.1.25) 673 0 R (equation.1.26) 674 0 R (equation.1.3) 607 0 R (equation.1.4) 608 0 R (equation.1.4a) 609 0 R (equation.1.4b) 610 0 R] +/Limits [(equation.1.25) (equation.1.4b)] >> endobj 998 0 obj << -/Names [(equation.5.2) 837 0 R (equation.5.20) 896 0 R (equation.5.3) 838 0 R (equation.5.4) 843 0 R (equation.5.5) 844 0 R (equation.5.5a) 845 0 R] -/Limits [(equation.5.2) (equation.5.5a)] +/Names [(equation.1.5) 616 0 R (equation.1.6) 617 0 R (equation.1.7) 618 0 R (equation.1.7a) 619 0 R (equation.1.7b) 620 0 R (equation.1.7c) 621 0 R] +/Limits [(equation.1.5) (equation.1.7c)] >> endobj 999 0 obj << -/Names [(equation.5.5b) 846 0 R (equation.5.6) 847 0 R (equation.5.6a) 848 0 R (equation.5.6b) 849 0 R (equation.5.6c) 850 0 R (equation.5.7) 851 0 R] -/Limits [(equation.5.5b) (equation.5.7)] +/Names [(equation.1.7d) 623 0 R (equation.1.8) 624 0 R (equation.1.8a) 625 0 R (equation.1.8b) 626 0 R (equation.1.8c) 627 0 R (equation.1.8d) 628 0 R] +/Limits [(equation.1.7d) (equation.1.8d)] >> endobj 1000 0 obj << -/Names [(equation.5.7a) 852 0 R (equation.5.7b) 853 0 R (equation.5.7c) 854 0 R (equation.5.8) 860 0 R (equation.5.8a) 861 0 R (equation.5.8b) 862 0 R] -/Limits [(equation.5.7a) (equation.5.8b)] +/Names [(equation.1.8e) 629 0 R (equation.1.8f) 630 0 R (equation.1.9) 635 0 R (equation.2.1) 679 0 R (equation.2.2) 680 0 R (equation.2.3) 681 0 R] +/Limits [(equation.1.8e) (equation.2.3)] >> endobj 1001 0 obj << -/Names [(equation.5.8c) 863 0 R (equation.5.9) 864 0 R (equation.6.1) 902 0 R (equation.6.1a) 903 0 R (equation.6.1b) 904 0 R (equation.6.1c) 905 0 R] -/Limits [(equation.5.8c) (equation.6.1c)] +/Names [(equation.2.4) 682 0 R (equation.2.5) 689 0 R (equation.2.6) 690 0 R (equation.2.7) 693 0 R (equation.2.7a) 695 0 R (equation.2.7b) 696 0 R] +/Limits [(equation.2.4) (equation.2.7b)] >> endobj 1002 0 obj << -/Names [(equation.6.2) 906 0 R (equation.6.3) 907 0 R (equation.6.4) 912 0 R (equation.6.4a) 913 0 R (equation.6.4b) 914 0 R (equation.6.4c) 915 0 R] -/Limits [(equation.6.2) (equation.6.4c)] +/Names [(equation.3.1) 702 0 R (equation.3.10) 725 0 R (equation.3.10a) 726 0 R (equation.3.10b) 727 0 R (equation.3.11) 733 0 R (equation.3.12) 734 0 R] +/Limits [(equation.3.1) (equation.3.12)] >> endobj 1003 0 obj << -/Names [(equation.6.4d) 916 0 R (equation.6.4e) 917 0 R (equation.6.4f) 918 0 R (equation.6.4g) 919 0 R (equation.6.5) 920 0 R (equation.6.6) 921 0 R] -/Limits [(equation.6.4d) (equation.6.6)] +/Names [(equation.3.12a) 735 0 R (equation.3.12b) 736 0 R (equation.3.13) 737 0 R (equation.3.14) 738 0 R (equation.3.14a) 739 0 R (equation.3.14b) 740 0 R] +/Limits [(equation.3.12a) (equation.3.14b)] >> endobj 1004 0 obj << -/Names [(equation.6.7) 927 0 R (page.0) 440 0 R (page.1) 452 0 R (page.10) 653 0 R (page.11) 661 0 R (page.12) 670 0 R] -/Limits [(equation.6.7) (page.12)] +/Names [(equation.3.15) 741 0 R (equation.3.16) 747 0 R (equation.3.17) 748 0 R (equation.3.18) 749 0 R (equation.3.19) 750 0 R (equation.3.2) 703 0 R] +/Limits [(equation.3.15) (equation.3.2)] >> endobj 1005 0 obj << -/Names [(page.13) 684 0 R (page.14) 699 0 R (page.15) 715 0 R (page.16) 729 0 R (page.17) 742 0 R (page.18) 748 0 R] -/Limits [(page.13) (page.18)] +/Names [(equation.3.20) 752 0 R (equation.3.21) 753 0 R (equation.3.22) 760 0 R (equation.3.23) 761 0 R (equation.3.3) 704 0 R (equation.3.3a) 705 0 R] +/Limits [(equation.3.20) (equation.3.3a)] >> endobj 1006 0 obj << -/Names [(page.19) 772 0 R (page.2) 488 0 R (page.20) 789 0 R (page.21) 801 0 R (page.22) 810 0 R (page.23) 835 0 R] -/Limits [(page.19) (page.23)] +/Names [(equation.3.3b) 706 0 R (equation.3.4) 707 0 R (equation.3.4a) 708 0 R (equation.3.4b) 709 0 R (equation.3.4c) 710 0 R (equation.3.5) 711 0 R] +/Limits [(equation.3.3b) (equation.3.5)] >> endobj 1007 0 obj << -/Names [(page.24) 842 0 R (page.25) 859 0 R (page.26) 871 0 R (page.27) 881 0 R (page.28) 889 0 R (page.29) 901 0 R] -/Limits [(page.24) (page.29)] +/Names [(equation.3.6) 718 0 R (equation.3.7) 719 0 R (equation.3.7a) 720 0 R (equation.3.7b) 721 0 R (equation.3.7c) 722 0 R (equation.3.8) 723 0 R] +/Limits [(equation.3.6) (equation.3.8)] >> endobj 1008 0 obj << -/Names [(page.3) 535 0 R (page.30) 911 0 R (page.31) 926 0 R (page.4) 577 0 R (page.5) 585 0 R (page.6) 590 0 R] -/Limits [(page.3) (page.6)] +/Names [(equation.3.9) 724 0 R (equation.4.1) 767 0 R (equation.4.10) 811 0 R (equation.4.11) 812 0 R (equation.4.12) 819 0 R (equation.4.13) 820 0 R] +/Limits [(equation.3.9) (equation.4.13)] >> endobj 1009 0 obj << -/Names [(page.7) 604 0 R (page.8) 622 0 R (page.9) 633 0 R (section*.3) 490 0 R (section.1.1) 6 0 R (section.1.2) 18 0 R] -/Limits [(page.7) (section.1.2)] +/Names [(equation.4.14) 821 0 R (equation.4.15) 822 0 R (equation.4.16) 832 0 R (equation.4.17) 833 0 R (equation.4.18) 835 0 R (equation.4.18a) 836 0 R] +/Limits [(equation.4.14) (equation.4.18a)] >> endobj 1010 0 obj << -/Names [(section.1.3) 30 0 R (section.1.4) 46 0 R (section.1.5) 50 0 R (section.1.6) 62 0 R (section.1.7) 74 0 R (section.2.1) 102 0 R] -/Limits [(section.1.3) (section.2.1)] +/Names [(equation.4.18b) 837 0 R (equation.4.18c) 838 0 R (equation.4.18d) 839 0 R (equation.4.2) 768 0 R (equation.4.3) 770 0 R (equation.4.3a) 772 0 R] +/Limits [(equation.4.18b) (equation.4.3a)] >> endobj 1011 0 obj << -/Names [(section.2.2) 114 0 R (section.2.3) 134 0 R (section.3.1) 146 0 R (section.3.2) 150 0 R (section.3.3) 162 0 R (section.3.4) 182 0 R] -/Limits [(section.2.2) (section.3.4)] +/Names [(equation.4.3b) 773 0 R (equation.4.3c) 774 0 R (equation.4.4) 790 0 R (equation.4.4a) 791 0 R (equation.4.4b) 792 0 R (equation.4.5) 793 0 R] +/Limits [(equation.4.3b) (equation.4.5)] >> endobj 1012 0 obj << -/Names [(section.3.5) 198 0 R (section.3.6) 210 0 R (section.4.1) 242 0 R (section.4.2) 270 0 R (section.4.3) 278 0 R (section.4.4) 294 0 R] -/Limits [(section.3.5) (section.4.4)] +/Names [(equation.4.6) 795 0 R (equation.4.6a) 796 0 R (equation.4.6b) 797 0 R (equation.4.6c) 799 0 R (equation.4.6d) 800 0 R (equation.4.6e) 801 0 R] +/Limits [(equation.4.6) (equation.4.6e)] >> endobj 1013 0 obj << -/Names [(section.5.1) 310 0 R (section.5.2) 346 0 R (section.5.3) 366 0 R (section.6.1) 398 0 R (section.6.2) 410 0 R (subsection.1.1.1) 10 0 R] -/Limits [(section.5.1) (subsection.1.1.1)] +/Names [(equation.4.7) 802 0 R (equation.4.8) 807 0 R (equation.4.8a) 808 0 R (equation.4.8b) 809 0 R (equation.4.9) 810 0 R (equation.5.1) 853 0 R] +/Limits [(equation.4.7) (equation.5.1)] >> endobj 1014 0 obj << -/Names [(subsection.1.1.2) 14 0 R (subsection.1.2.1) 22 0 R (subsection.1.2.2) 26 0 R (subsection.1.3.1) 34 0 R (subsection.1.3.2) 38 0 R (subsection.1.3.3) 42 0 R] -/Limits [(subsection.1.1.2) (subsection.1.3.3)] +/Names [(equation.5.10) 882 0 R (equation.5.11) 889 0 R (equation.5.12) 890 0 R (equation.5.13) 891 0 R (equation.5.14) 899 0 R (equation.5.14a) 900 0 R] +/Limits [(equation.5.10) (equation.5.14a)] >> endobj 1015 0 obj << -/Names [(subsection.1.5.1) 54 0 R (subsection.1.5.2) 58 0 R (subsection.1.6.1) 66 0 R (subsection.1.6.2) 70 0 R (subsection.1.7.1) 78 0 R (subsection.1.7.2) 82 0 R] -/Limits [(subsection.1.5.1) (subsection.1.7.2)] +/Names [(equation.5.14b) 901 0 R (equation.5.15) 902 0 R (equation.5.16) 907 0 R (equation.5.17) 908 0 R (equation.5.18) 909 0 R (equation.5.18a) 910 0 R] +/Limits [(equation.5.14b) (equation.5.18a)] >> endobj 1016 0 obj << -/Names [(subsection.1.7.3) 86 0 R (subsection.1.7.4) 90 0 R (subsection.1.7.5) 94 0 R (subsection.2.1.1) 106 0 R (subsection.2.1.2) 110 0 R (subsection.2.2.1) 118 0 R] -/Limits [(subsection.1.7.3) (subsection.2.2.1)] +/Names [(equation.5.18b) 911 0 R (equation.5.19) 912 0 R (equation.5.2) 854 0 R (equation.5.20) 913 0 R (equation.5.3) 855 0 R (equation.5.4) 861 0 R] +/Limits [(equation.5.18b) (equation.5.4)] >> endobj 1017 0 obj << -/Names [(subsection.2.2.2) 122 0 R (subsection.2.2.3) 126 0 R (subsection.2.2.4) 130 0 R (subsection.2.3.1) 138 0 R (subsection.3.2.1) 154 0 R (subsection.3.2.2) 158 0 R] -/Limits [(subsection.2.2.2) (subsection.3.2.2)] +/Names [(equation.5.5) 862 0 R (equation.5.5a) 863 0 R (equation.5.5b) 864 0 R (equation.5.6) 865 0 R (equation.5.6a) 866 0 R (equation.5.6b) 867 0 R] +/Limits [(equation.5.5) (equation.5.6b)] >> endobj 1018 0 obj << -/Names [(subsection.3.3.1) 166 0 R (subsection.3.3.2) 170 0 R (subsection.3.3.3) 174 0 R (subsection.3.3.4) 178 0 R (subsection.3.4.1) 186 0 R (subsection.3.4.2) 190 0 R] -/Limits [(subsection.3.3.1) (subsection.3.4.2)] +/Names [(equation.5.6c) 868 0 R (equation.5.7) 869 0 R (equation.5.7a) 870 0 R (equation.5.7b) 871 0 R (equation.5.7c) 872 0 R (equation.5.8) 877 0 R] +/Limits [(equation.5.6c) (equation.5.8)] >> endobj 1019 0 obj << -/Names [(subsection.3.4.3) 194 0 R (subsection.3.5.1) 202 0 R (subsection.3.5.2) 206 0 R (subsection.3.6.1) 214 0 R (subsection.3.6.2) 218 0 R (subsection.3.6.3) 222 0 R] -/Limits [(subsection.3.4.3) (subsection.3.6.3)] +/Names [(equation.5.8a) 878 0 R (equation.5.8b) 879 0 R (equation.5.8c) 880 0 R (equation.5.9) 881 0 R (equation.6.1) 919 0 R (equation.6.1a) 920 0 R] +/Limits [(equation.5.8a) (equation.6.1a)] >> endobj 1020 0 obj << -/Names [(subsection.3.6.4) 226 0 R (subsection.3.6.5) 230 0 R (subsection.3.6.6) 234 0 R (subsection.4.1.1) 246 0 R (subsection.4.1.2) 250 0 R (subsection.4.1.3) 254 0 R] -/Limits [(subsection.3.6.4) (subsection.4.1.3)] +/Names [(equation.6.1b) 921 0 R (equation.6.1c) 922 0 R (equation.6.2) 923 0 R (equation.6.3) 924 0 R (equation.6.4) 930 0 R (equation.6.4a) 931 0 R] +/Limits [(equation.6.1b) (equation.6.4a)] >> endobj 1021 0 obj << -/Names [(subsection.4.1.4) 258 0 R (subsection.4.1.5) 262 0 R (subsection.4.1.6) 266 0 R (subsection.4.2.1) 274 0 R (subsection.4.3.1) 282 0 R (subsection.4.3.2) 286 0 R] -/Limits [(subsection.4.1.4) (subsection.4.3.2)] +/Names [(equation.6.4b) 932 0 R (equation.6.4c) 933 0 R (equation.6.4d) 934 0 R (equation.6.4e) 935 0 R (equation.6.4f) 936 0 R (equation.6.4g) 937 0 R] +/Limits [(equation.6.4b) (equation.6.4g)] >> endobj 1022 0 obj << -/Names [(subsection.4.3.3) 290 0 R (subsection.4.4.1) 298 0 R (subsection.4.4.2) 302 0 R (subsection.5.1.1) 314 0 R (subsection.5.1.2) 318 0 R (subsection.5.1.3) 322 0 R] -/Limits [(subsection.4.3.3) (subsection.5.1.3)] +/Names [(equation.6.5) 938 0 R (equation.6.6) 939 0 R (equation.6.7) 944 0 R (page.0) 444 0 R (page.1) 456 0 R (page.10) 655 0 R] +/Limits [(equation.6.5) (page.10)] >> endobj 1023 0 obj << -/Names [(subsection.5.1.4) 326 0 R (subsection.5.1.5) 330 0 R (subsection.5.1.6) 334 0 R (subsection.5.1.7) 338 0 R (subsection.5.1.8) 342 0 R (subsection.5.2.1) 350 0 R] -/Limits [(subsection.5.1.4) (subsection.5.2.1)] +/Names [(page.11) 672 0 R (page.12) 678 0 R (page.13) 688 0 R (page.14) 701 0 R (page.15) 716 0 R (page.16) 732 0 R] +/Limits [(page.11) (page.16)] >> endobj 1024 0 obj << -/Names [(subsection.5.2.2) 354 0 R (subsection.5.2.3) 358 0 R (subsection.5.2.4) 362 0 R (subsection.5.3.1) 370 0 R (subsection.5.3.2) 374 0 R (subsection.5.3.3) 378 0 R] -/Limits [(subsection.5.2.2) (subsection.5.3.3)] +/Names [(page.17) 746 0 R (page.18) 759 0 R (page.19) 766 0 R (page.2) 492 0 R (page.20) 789 0 R (page.21) 806 0 R] +/Limits [(page.17) (page.21)] >> endobj 1025 0 obj << -/Names [(subsection.5.3.4) 382 0 R (subsection.5.3.5) 386 0 R (subsection.5.3.6) 390 0 R (subsection.6.1.1) 402 0 R (subsection.6.1.2) 406 0 R (subsection.6.2.1) 414 0 R] -/Limits [(subsection.5.3.4) (subsection.6.2.1)] +/Names [(page.22) 818 0 R (page.23) 827 0 R (page.24) 852 0 R (page.25) 860 0 R (page.26) 876 0 R (page.27) 888 0 R] +/Limits [(page.22) (page.27)] >> endobj 1026 0 obj << -/Names [(subsection.6.2.2) 418 0 R (subsection.6.2.3) 422 0 R (subsection.6.2.4) 426 0 R (subsection.6.2.5) 430 0 R (subsubsection*.10) 817 0 R (subsubsection*.4) 628 0 R] -/Limits [(subsection.6.2.2) (subsubsection*.4)] +/Names [(page.28) 898 0 R (page.29) 906 0 R (page.3) 538 0 R (page.30) 918 0 R (page.31) 929 0 R (page.32) 943 0 R] +/Limits [(page.28) (page.32)] >> endobj 1027 0 obj << -/Names [(subsubsection*.5) 634 0 R (subsubsection*.6) 734 0 R (subsubsection*.7) 751 0 R (subsubsection*.8) 777 0 R (subsubsection*.9) 811 0 R] -/Limits [(subsubsection*.5) (subsubsection*.9)] +/Names [(page.4) 582 0 R (page.5) 590 0 R (page.6) 595 0 R (page.7) 615 0 R (page.8) 634 0 R (page.9) 644 0 R] +/Limits [(page.4) (page.9)] >> endobj 1028 0 obj << -/Kids [974 0 R 975 0 R 976 0 R 977 0 R 978 0 R 979 0 R] -/Limits [(Doc-Start) (equation.1.5a)] +/Names [(section*.3) 494 0 R (section.1.1) 6 0 R (section.1.2) 10 0 R (section.1.3) 22 0 R (section.1.4) 34 0 R (section.1.5) 50 0 R] +/Limits [(section*.3) (section.1.5)] >> endobj 1029 0 obj << -/Kids [980 0 R 981 0 R 982 0 R 983 0 R 984 0 R 985 0 R] -/Limits [(equation.1.5b) (equation.3.16)] +/Names [(section.1.6) 54 0 R (section.1.7) 66 0 R (section.1.8) 78 0 R (section.2.1) 106 0 R (section.2.2) 118 0 R (section.2.3) 138 0 R] +/Limits [(section.1.6) (section.2.3)] >> endobj 1030 0 obj << -/Kids [986 0 R 987 0 R 988 0 R 989 0 R 990 0 R 991 0 R] -/Limits [(equation.3.17) (equation.4.18c)] +/Names [(section.3.1) 150 0 R (section.3.2) 154 0 R (section.3.3) 166 0 R (section.3.4) 186 0 R (section.3.5) 202 0 R (section.3.6) 214 0 R] +/Limits [(section.3.1) (section.3.6)] >> endobj 1031 0 obj << -/Kids [992 0 R 993 0 R 994 0 R 995 0 R 996 0 R 997 0 R] -/Limits [(equation.4.18d) (equation.5.19)] +/Names [(section.4.1) 246 0 R (section.4.2) 274 0 R (section.4.3) 282 0 R (section.4.4) 298 0 R (section.5.1) 314 0 R (section.5.2) 350 0 R] +/Limits [(section.4.1) (section.5.2)] >> endobj 1032 0 obj << -/Kids [998 0 R 999 0 R 1000 0 R 1001 0 R 1002 0 R 1003 0 R] -/Limits [(equation.5.2) (equation.6.6)] +/Names [(section.5.3) 370 0 R (section.6.1) 402 0 R (section.6.2) 414 0 R (subsection.1.2.1) 14 0 R (subsection.1.2.2) 18 0 R (subsection.1.3.1) 26 0 R] +/Limits [(section.5.3) (subsection.1.3.1)] >> endobj 1033 0 obj << -/Kids [1004 0 R 1005 0 R 1006 0 R 1007 0 R 1008 0 R 1009 0 R] -/Limits [(equation.6.7) (section.1.2)] +/Names [(subsection.1.3.2) 30 0 R (subsection.1.4.1) 38 0 R (subsection.1.4.2) 42 0 R (subsection.1.4.3) 46 0 R (subsection.1.6.1) 58 0 R (subsection.1.6.2) 62 0 R] +/Limits [(subsection.1.3.2) (subsection.1.6.2)] >> endobj 1034 0 obj << -/Kids [1010 0 R 1011 0 R 1012 0 R 1013 0 R 1014 0 R 1015 0 R] -/Limits [(section.1.3) (subsection.1.7.2)] +/Names [(subsection.1.7.1) 70 0 R (subsection.1.7.2) 74 0 R (subsection.1.8.1) 82 0 R (subsection.1.8.2) 86 0 R (subsection.1.8.3) 90 0 R (subsection.1.8.4) 94 0 R] +/Limits [(subsection.1.7.1) (subsection.1.8.4)] >> endobj 1035 0 obj << -/Kids [1016 0 R 1017 0 R 1018 0 R 1019 0 R 1020 0 R 1021 0 R] -/Limits [(subsection.1.7.3) (subsection.4.3.2)] +/Names [(subsection.1.8.5) 98 0 R (subsection.2.1.1) 110 0 R (subsection.2.1.2) 114 0 R (subsection.2.2.1) 122 0 R (subsection.2.2.2) 126 0 R (subsection.2.2.3) 130 0 R] +/Limits [(subsection.1.8.5) (subsection.2.2.3)] >> endobj 1036 0 obj << -/Kids [1022 0 R 1023 0 R 1024 0 R 1025 0 R 1026 0 R 1027 0 R] -/Limits [(subsection.4.3.3) (subsubsection*.9)] +/Names [(subsection.2.2.4) 134 0 R (subsection.2.3.1) 142 0 R (subsection.3.2.1) 158 0 R (subsection.3.2.2) 162 0 R (subsection.3.3.1) 170 0 R (subsection.3.3.2) 174 0 R] +/Limits [(subsection.2.2.4) (subsection.3.3.2)] >> endobj 1037 0 obj << -/Kids [1028 0 R 1029 0 R 1030 0 R 1031 0 R 1032 0 R 1033 0 R] -/Limits [(Doc-Start) (section.1.2)] +/Names [(subsection.3.3.3) 178 0 R (subsection.3.3.4) 182 0 R (subsection.3.4.1) 190 0 R (subsection.3.4.2) 194 0 R (subsection.3.4.3) 198 0 R (subsection.3.5.1) 206 0 R] +/Limits [(subsection.3.3.3) (subsection.3.5.1)] >> endobj 1038 0 obj << -/Kids [1034 0 R 1035 0 R 1036 0 R] -/Limits [(section.1.3) (subsubsection*.9)] +/Names [(subsection.3.5.2) 210 0 R (subsection.3.6.1) 218 0 R (subsection.3.6.2) 222 0 R (subsection.3.6.3) 226 0 R (subsection.3.6.4) 230 0 R (subsection.3.6.5) 234 0 R] +/Limits [(subsection.3.5.2) (subsection.3.6.5)] >> endobj 1039 0 obj << -/Kids [1037 0 R 1038 0 R] -/Limits [(Doc-Start) (subsubsection*.9)] +/Names [(subsection.3.6.6) 238 0 R (subsection.4.1.1) 250 0 R (subsection.4.1.2) 254 0 R (subsection.4.1.3) 258 0 R (subsection.4.1.4) 262 0 R (subsection.4.1.5) 266 0 R] +/Limits [(subsection.3.6.6) (subsection.4.1.5)] >> endobj 1040 0 obj << -/Dests 1039 0 R +/Names [(subsection.4.1.6) 270 0 R (subsection.4.2.1) 278 0 R (subsection.4.3.1) 286 0 R (subsection.4.3.2) 290 0 R (subsection.4.3.3) 294 0 R (subsection.4.4.1) 302 0 R] +/Limits [(subsection.4.1.6) (subsection.4.4.1)] >> endobj 1041 0 obj << -/Type /Catalog -/Pages 972 0 R -/Outlines 973 0 R -/Names 1040 0 R -/PageMode/UseOutlines/PageLabels<>1<>]>> -/OpenAction 433 0 R +/Names [(subsection.4.4.2) 306 0 R (subsection.5.1.1) 318 0 R (subsection.5.1.2) 322 0 R (subsection.5.1.3) 326 0 R (subsection.5.1.4) 330 0 R (subsection.5.1.5) 334 0 R] +/Limits [(subsection.4.4.2) (subsection.5.1.5)] >> endobj 1042 0 obj << +/Names [(subsection.5.1.6) 338 0 R (subsection.5.1.7) 342 0 R (subsection.5.1.8) 346 0 R (subsection.5.2.1) 354 0 R (subsection.5.2.2) 358 0 R (subsection.5.2.3) 362 0 R] +/Limits [(subsection.5.1.6) (subsection.5.2.3)] +>> endobj +1043 0 obj << +/Names [(subsection.5.2.4) 366 0 R (subsection.5.3.1) 374 0 R (subsection.5.3.2) 378 0 R (subsection.5.3.3) 382 0 R (subsection.5.3.4) 386 0 R (subsection.5.3.5) 390 0 R] +/Limits [(subsection.5.2.4) (subsection.5.3.5)] +>> endobj +1044 0 obj << +/Names [(subsection.5.3.6) 394 0 R (subsection.6.1.1) 406 0 R (subsection.6.1.2) 410 0 R (subsection.6.2.1) 418 0 R (subsection.6.2.2) 422 0 R (subsection.6.2.3) 426 0 R] +/Limits [(subsection.5.3.6) (subsection.6.2.3)] +>> endobj +1045 0 obj << +/Names [(subsection.6.2.4) 430 0 R (subsection.6.2.5) 434 0 R (subsubsection*.10) 834 0 R (subsubsection*.4) 645 0 R (subsubsection*.5) 647 0 R (subsubsection*.6) 751 0 R] +/Limits [(subsection.6.2.4) (subsubsection*.6)] +>> endobj +1046 0 obj << +/Names [(subsubsection*.7) 769 0 R (subsubsection*.8) 794 0 R (subsubsection*.9) 828 0 R] +/Limits [(subsubsection*.7) (subsubsection*.9)] +>> endobj +1047 0 obj << +/Kids [991 0 R 992 0 R 993 0 R 994 0 R 995 0 R 996 0 R] +/Limits [(Doc-Start) (equation.1.24)] +>> endobj +1048 0 obj << +/Kids [997 0 R 998 0 R 999 0 R 1000 0 R 1001 0 R 1002 0 R] +/Limits [(equation.1.25) (equation.3.12)] +>> endobj +1049 0 obj << +/Kids [1003 0 R 1004 0 R 1005 0 R 1006 0 R 1007 0 R 1008 0 R] +/Limits [(equation.3.12a) (equation.4.13)] +>> endobj +1050 0 obj << +/Kids [1009 0 R 1010 0 R 1011 0 R 1012 0 R 1013 0 R 1014 0 R] +/Limits [(equation.4.14) (equation.5.14a)] +>> endobj +1051 0 obj << +/Kids [1015 0 R 1016 0 R 1017 0 R 1018 0 R 1019 0 R 1020 0 R] +/Limits [(equation.5.14b) (equation.6.4a)] +>> endobj +1052 0 obj << +/Kids [1021 0 R 1022 0 R 1023 0 R 1024 0 R 1025 0 R 1026 0 R] +/Limits [(equation.6.4b) (page.32)] +>> endobj +1053 0 obj << +/Kids [1027 0 R 1028 0 R 1029 0 R 1030 0 R 1031 0 R 1032 0 R] +/Limits [(page.4) (subsection.1.3.1)] +>> endobj +1054 0 obj << +/Kids [1033 0 R 1034 0 R 1035 0 R 1036 0 R 1037 0 R 1038 0 R] +/Limits [(subsection.1.3.2) (subsection.3.6.5)] +>> endobj +1055 0 obj << +/Kids [1039 0 R 1040 0 R 1041 0 R 1042 0 R 1043 0 R 1044 0 R] +/Limits [(subsection.3.6.6) (subsection.6.2.3)] +>> endobj +1056 0 obj << +/Kids [1045 0 R 1046 0 R] +/Limits [(subsection.6.2.4) (subsubsection*.9)] +>> endobj +1057 0 obj << +/Kids [1047 0 R 1048 0 R 1049 0 R 1050 0 R 1051 0 R 1052 0 R] +/Limits [(Doc-Start) (page.32)] +>> endobj +1058 0 obj << +/Kids [1053 0 R 1054 0 R 1055 0 R 1056 0 R] +/Limits [(page.4) (subsubsection*.9)] +>> endobj +1059 0 obj << +/Kids [1057 0 R 1058 0 R] +/Limits [(Doc-Start) (subsubsection*.9)] +>> endobj +1060 0 obj << +/Dests 1059 0 R +>> endobj +1061 0 obj << +/Type /Catalog +/Pages 989 0 R +/Outlines 990 0 R +/Names 1060 0 R +/PageMode/UseOutlines/PageLabels<>1<>]>> 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+0000308399 00000 n +0000308533 00000 n +0000308631 00000 n +0000308749 00000 n +0000308855 00000 n +0000308946 00000 n +0000308986 00000 n +0000309157 00000 n trailer -<< /Size 1043 -/Root 1041 0 R -/Info 1042 0 R -/ID [ ] >> +<< /Size 1063 +/Root 1061 0 R +/Info 1062 0 R +/ID [<79F4F0E237AFB41D7852B2DE28899CFD> <79F4F0E237AFB41D7852B2DE28899CFD>] >> startxref -305692 +309466 %%EOF diff --git a/document.tex b/document.tex index cde4289..c5967c0 100644 --- a/document.tex +++ b/document.tex @@ -23,7 +23,7 @@ \title{Stochastische Signale und Systeme} \subtitle{Zusammenfassung Formeln} -\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 0.9.6.2 - 25.09.2012} +\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 0.9.7 - 26.09.2012} \maketitle \newpage @@ -40,7 +40,21 @@ Fehler und Verbesserungen bitte an studium@daniel-thiem.de senden oder als Issue bei \url{https://github.com/Tyde/stosigsysfs/issues} melden. Der Quelltext dieser Formelsammlung ist auf \url{https://github.com/Tyde/stosigsysfs} und darf gerne erweitert werden. \chapter{Kombinatorik \& reine Stochastik} - +\section{Megenlehre} +\begin{subequations} +\begin{align} +P(\overline{A\cup B})&=P(\overline{A} \cap \overline{B})\\ +P(\overline{A\cap B})&=P(\overline{A} \cup \overline{B}) \\ +P(A\cup (A \cap B))&=P(A) \\ +P(A\cap (A \cup B))&=P(A) \\ +P(\overline{\bar{A}})&=P(A) \\ +P\left(\bigcup\limits_{i=0}^n A_i\right)&=\sum\limits_{i=0}^n P(A_i) +\end{align} +\end{subequations} +Falls $A$ und $B$ stochastisch unabhngig: +\begin{equation} +P(A\cap B)=P(A)\cdot P(B) +\end{equation} \section{Wahrscheinlichkeitsdichtefunktion} Sei $F_X(x)$ die Verteilungsfunktion der Zufallsvariablen $X$ \begin{equation}