Kapitel 5

2.
a)
b) X has marginal density as hypergeometric distribution with N = 7, n = 4 and
r = 3.
Y has marginal density as hypergeometric distribution with N = 7, n = 4 and r
= 4
c) No, they are not independent. Show that there are values where f(x,y) are
not equal to f(x)f(y)

8.
a) c = 1/6640
b) 37.35%
c) f(x) = c*(8x+6)
   f(y) = c*40*(2y+81)
d) P(Y >= 1) = 84/166
e) P(X >= 20) = 123/166
f)

20.
a) negative, warmer temperature gives a faster ignition.
b) E(X) = 6580/249
   E(Y) = 502/498
   E(XY) = 6620/249
   C(X,Y) = - 3200/62001

42.
a) (y-1)/ln(y)
b) 1/(2*ln(2))
c) x/2
d) 3/8

Kapitel 12

1. Degree 1. 

3. (a) sum_i x_1i = 6, sum_i x_2i = 25, sum_i x_1i*x_2i = 50, sum_i x_1i*y_i =
44, sum_i x_1i^2 = 20, sum_i x_2i^2 = 209, sum_i y_i = 24, sum_i x_2i y_i =
200

5. b0 + b1*x1 + b2*x2 + b3*x3, b3 = b12, x3 = x1*x2

7. (a) | 8      464.4    | * | b0 | = | 46.2    |
       | 464.4  32089.96 |   | b1 |   | 3173.17 |
	 (b) b0 = 0.2177, b1 = 0.0957

14.
a) [1, 0, 8 ; 1,2,9; 1,4,8]
b) [3,6,25 ; 6,20,50 ; 25,50,209]
c) [24;44;200]
d) Compare normal equations with exercise 3
e) Multiply with X'X and see that the result is the identity matrix 
f) Insert the given values and see that they add up

38.
[1,1,1;1,2,4;1,3,9;1,4,16;1,5,25;1,6,36;1,7,49]

40. 
T = 3.6
p = 13.07%
If your answer is not exactly the same it might be due to roundoff.

42.
[26.280, 50.254]
If your answer is not exactly the same it might be due to roundoff.




Kapitel 13

4. 
a) H0: mu1 = mu2 = mu3 = mu4
   H1: mu_i1 different from mu_i2, some 1 <= i1, i2 <= 4
b) T = 6.3343, p = 0.0017
c) För minst två av grupperna skiljer sig medelvärdena åt.




Kapitel 14

4.
H0: (alphabeta)ij = 0, i=1,2,3, j=1,2,3
H1: (alphabeta)ij är skilt från noll, för något par (i,j)

6.
T = 1.0405
p = 0.4138

8.
T = 130.24
p = 2*10^-11

26.
16, 32, 128

34.
Jämför med tabell 14.8
(a) 
index i vektorerna motsvarar [A B AB C AC BC ABC D AD BD ABD CD ACD BCD ABCD]:
SS = MS = [133.66 4.35 2.53 101.53 3.5115 9.9015 1.2015 1.3615 1.2015 1.2015
5.61 4.6516 1.2015 5.2815 4.6515]
SSE = 4.15
F = MS/(SSE/2^4) = [515.32 16.78 9.76 391.45 13.54 38.17 4.63 5.25 4.63 4.63 21.63 17.99 4.63
20.36 17.93]
(b) 
index i vektorerna motsvarar [A B AB C AC BC D AD BD CD]:
SS = MS = [133.66 4.35 2.53 101.53 3.5115 9.9015 1.3615 1.2015 1.2015 4.6516]
SSE = 22.0960
F = MS/(SSE/(2^4+5)) = [127.0302 4.1342 2.4045 96.4939 3.3373 9.4104 1.2940
1.1419 1.1419 4.4209] 
(c)
index i vektorerna motsvarar [A B AB C AC BC ABC D AD BD ACD]:
SS = MS = [133.66 4.35 2.53 101.53 3.5115 9.9015 1.2015 1.3615 1.2015 1.2015
1.2015]
SSE = 24.345
F = MS/(SSE/(2^4+4)) = [109.8062 3.5737 2.0785 83.4104 2.8848 0.9871 1.1185
0.9871 0.9871 0.9871]