Lösungen / Statistik 1/12

Lösungen / Statistik 1/12

Remove @ "Global`*" D

1.

p = 2 • 6 * 2 • 36 * 1 • 6

€€€€€€€€€€ 1 324

N @ % D 0.00308642

2.

p1 = 97 • 213

€€€€€€€€€€ 97 213

N @ % D 0.455399

p1 = 97 • 148

€€€€€€€€€€ 97 148

N @ % D 0.655405

3.

Ÿ a

f @ t_ D := 22 + 16 t + 3 t

; g @ t_ D := 21 + 10 t + t

LM2Sta12.nb 1

Plot @8 f @ t D , g @ t D< , 8 t, 0, 4 <D ;

1 2 3 4

20 40 60 80 100 120

Limit @ g @ t D • f @ t D , t ® Infinity D

€€€€ 1 3

Ÿ b

f @ t_ D := 2 E ^ t;

g @ t_ D := 1 • 2 E ^ H t • 2 L ;

Plot @8 f @ t D , g @ t D< , 8 t, 0, 4 <D ;

1 2 3 4

10 20 30 40 50 60 70

Limit @ g @ t D • f @ t D , t ® Infinity D 0

Ÿ c

p = 289 • 1000

€€€€€€€€€€€€€ 289 1000

N @ % D 0.289

LM2Sta12.nb 2

4.

Ÿ a

r1g2 = 4 • 10 * 3 • 9;

g1r2 = 2 • 10 * 4 • 9;

r1g2 + g1r2

€€€€ 2 9

N @ % D 0.222222

Ÿ b

3 ! 6

r = 4; j = 2; v = 3; n = 1;

r1j2v3 = r * j * v • H 10 * 9 * 8 L ; r1v2j3 = r * v * j • H 10 * 9 * 8 L ; r1j2v3 == r1v2j3

True

nF = r * v * j • H 10 * 9 * 8 L ; vF = r * n * j • H 10 * 9 * 8 L ; jF = r * n * v • H 10 * 9 * 8 L ; nF = r * j * v • H 10 * 9 * 8 L ; p = 6 H nF + vF + jF + nF L

€€€€€€€ 17 30

N @ % D 0.566667

5. Treppenfunktion

Remove @ "Global`*" D

LM2Sta12.nb 3

h @ x_ D := Sign @H Sign @ x D + 1 L • 2 D ; p @ 1 D = 1 • 6; t @ 1 D = 0;

p @ 2 D = 1 • 3; t @ 2 D = 2;

p @ 3 D = 1 • 12; t @ 3 D = 3;

p @ 4 D = 1 • 12; t @ 4 D = 5;

p @ 5 D = 1 • 3; t @ 5 D = 7;

F @ x_ D := Sum @ p @ k D h @ x - t @ k DD , 8 k, 1, 5 <D F @ x D

€€€€ 1

3 Sign @ 1 + Sign @ -7 + x DD + 1

€€€€€€€

12 Sign @ 1 + Sign @ -5 + x DD +

€€€€€€€ 1

12 Sign @ 1 + Sign @-3 + x DD + 1

€€€€ 3 Sign @ 1 + Sign @-2 + x DD + 1

€€€€ 6 Sign @ 1 + Sign @ x DD Plot @ F @ x D , 8 x, -2, 9 <D ;

-2 2 4 6 8

0.2 0.4 0.6 0.8 1

Table @8 t @ k D , F @ t @ k DD< , 8 k, 1, 5 <D •• N •• TableForm 0. 0.166667

2. 0.5

3. 0.583333 5. 0.666667

7. 1.

LM2Sta12.nb 4