Lösungen / Solutions

<< Statistics`DescriptiveStatistics`;
<< Statistics`DataManipulation`;
<< Graphics`Graphics`;

1

u = 100;  a = 50; b = a; c = a; ab = 30; bc = 25; ac = 20; 
    abc = 5;

aUbUc = a + b + c - ab - ac - ab + abc

u - abc

u - aUbUc

2

m = {{173, 177, 176, 175, 174}, 
{178, 177, 177, 173, 
          173}, 
{177, 169, 169, 179, 
          179}, 
{173, 183, 177, 178, 
          169}, 
{184, 185, 173, 177, 
          179}, 
{161, 183, 163, 168, 
          168}, 
{162, 173, 192, 158, 
          174}, 
{169, 192, 165, 183, 
          194}, 
{154, 182, 156, 187, 
          160}, 
{188, 181, 159, 175, 187}}

m // Transpose // MatrixForm

m = Flatten[m]

{Min[m], Max[m]}

BarChart[m];

r = Table[k - 2.5, {k, 152, 200, 5}]

r1 = Table[k, {k, 147, 200, 5}]

mr = RangeCounts[m, r]

BarChart[mr, BarLabels -> r1];

mNew = 
      Table[Table[r1[[k]], {j, 1, mr[[k]]}], {k, 1, Length[mr]}] // 
        Flatten

Length[mNew]

(172 + 177)/2

Union[LocationReport[mNew], DispersionReport[mNew]]

Union[LocationReport[mNew], DispersionReport[mNew]] // N

Union[LocationReport[m], DispersionReport[m]]

Union[LocationReport[m], DispersionReport[m]] // N

3

a

no1AndNo2 = (36 - 4) (36 - 4)/(36*36)

no1AndNo2N = no1AndNo2 // N

minKing = 1 - no1AndNo2

minKingN = 1 - no1AndNo2N

b

Red, but no king

red1 = 16/36 * 16/36

red1N = red1 // N

red2 = red1

red1And2 = 16/36  *16/36

red1And2N = red1And2  // N

red1OrRed2OrRed1And2 = red1 + red2 + red1And2

red1OrRed2OrRed1And2 // N

King

minKing = 1 - no1AndNo2

minKing // N

Red or king

red1OrRed2OrRed1And2 + minKing

red1OrRed2OrRed1And2 + minKing // N

Control

r1b2Ub1r2Ur1r2Ukb1nkb2Unkb1kb2Ukb1kb2 = 
3*(1/
                2)^2 + 2*(2/36*16/36) + (2/36)^2

c

Once a king or queen

kingQueenBlack1AndRed2 = 4/36*18/36

kingQueenBlack1AndRed2 // N

kingQueenBlack2AndRed1 = kingQueenBlack1AndRed2

kingQueenBlack1AndRed2 + kingQueenBlack2AndRed1 // N

kingQueenRed1AndBlack2 = 4/36*14/36

kingQueenRed1AndBlack2 // N

kingQueenRed2AndBlack1 = kingQueenRed1AndBlack2

kingQueenRed2AndBlack1  //  N

kingQueenBlack1AndRed2 + kingQueenBlack2AndRed1 + 
      kingQueenRed1AndBlack2 + kingQueenRed2AndBlack1

kingQueenBlack1AndRed2 + kingQueenBlack2AndRed1 + 
        kingQueenRed1AndBlack2 + kingQueenRed2AndBlack1 // N

4

Auswählen und auf die 2 mal 10 Personen anordnen.
Choisir et ranger d'après les 2 fois 10 personnes.

all = 50^20

allDifferent = 50!/(50 - 20)!

notDifferent =  all - allDifferent

p = notDifferent/all

p  // N

5

a

Punkte zwischen die Marken 0 ... 100
Points entre les marques 0 ... 100

?Binomi*

comb = Binomial[100, 2]

Sum[k, {k, 1, 99}]

b

Punkte auf die Marken 1 ... 100
Points sur les marques 1 ... 100

solv = Binomial[100, 2]