In-Class Exercise Sheet 1 (Probability)

1: (a) 13/60 ; (b) 1/6 ; (c) 1/7, 1/5, 6/19 ; (d) 1/7 ; (e) 5/38

2: (a) 0.52 ; (b) 0.096 ; (c) 0.104, 0.228, 0.188

3: (a) 0.072, 0.096 ; (b) 0.416 ; (c) 0.282

In-Class Exercise Sheet 2 (Discrete Distributions)

1: (a) 3.4; (b) 2.24; (c) —; (d) 3.4 + a; (e) 2.24; (f) —; (g) 3.4a; (h) 2.24a^2

2: (a) 142.2, 56; (b) 146.866, 135.2; (c) 22.22, 25; (d) 142.2; (e) 32.666; (f) 23.333; (g) 56

In-Class Exercise Sheet 3 (Discrete and Continuous Distributions)

1: (a) p(0,0)=10/66, p(2,0)=3/66, p(0,2)=6/66, p(1,0)=15/66, p(0,1)=20/66, p(1,1)=12/66; (b) 1/2

2: (a) —; (b) 2x with 0<x<1; (c) 2y with 0<y<1; (d) 2/3; (e) 2/3

In-Class Exercise Sheet 4 (Special Distributions 1)

1: (a) 0.209 ; (b) 0.315 ; (c) 0.894

2: (a) 0.041 ; (b) 0.050 ; (c) 0.991

3: (a) 0.261 ; (b) 0.570 ; (c) 0.692

4: (a) 0.209 x 0.209 ; (b) 0.018 ; (c) 0.0004

5: (a) 0.000 ; (b) 0.977 ; (c) 0.023

6: (a) 0.987 ; (b) 0.327

7: (a) 0.412 ; (b) 0.327 ; (c) 0.177

In-Class Exercise Sheet 5 (Special Distributions 2)

1: (a) 1, 1 ; (b) (0,0.841), (2,0.136), (5,0.02275) ; (c) (0,0.841^2), (2,2*0.841*0.136), (4,0.136^2), ...

2: (a) 0.3 ; (b) 0.383 ; (c) 0.837

3: (a) 0.099 ; (b) 459.32, 576.68 ; (c) if independent 0.615, if perfectly dependent 0.582 ; (d) 0.626

In-Class Exercise Sheet 6 (Hypothesis Testing)

1: (a) reject ; (b) reject ; (c) 52.72, 53.85

2: (a) reject ; (b) reject

3: (a) fail to reject ; (b) 227.31 ; (c) 0.246 ; (d) —