MXB101
Worksheet 4
A) Questions for Group Work (compulsory)
The following 6 questions are meant to be solved in your group between Friday
Week 4 and Friday Week 5. Out of these 6 questions, questions 2 and 5 are part of
Assignment 2 and question 6 is part

MXB101
Worksheet 2
A) Questions for Group Work (compulsory)
The following 6 questions are meant to be solved in your group between Friday Week 2 and the
lecture on Wednesday Week 3. Out of these questions, questions 2, 3 and 4 are part of
Assignment 1, wh

MXB101: Worksheet Solutions Section 3
A) Questions for Group Work (compulsory)
1. Events: N := Nancy is within earshot of her pager (i.e., responds to her pager)
R := Ronald responds to his pager
Probabilities:
Pr ( N ) = 0.8, Pr ( R ) = 0.5 .
We want the

MXB101
Worksheet 1
A) Questions for Group Work (compulsory)
The following 6 questions are meant to be solved in your group between Friday Week 1 and
Wednesday Week 2. Out of these 6 questions, questions 3 and 6 are part of Assignment 1,
which is due by 8:

MXB101
Worksheet 3
A) Questions for Group Work (compulsory)
The following 5 questions are meant to be solved in your group between Friday Week 3
and Wednesday Week 4. Out of these 5 questions, questions 3, 4 and 5 are part of
Assignment 2, which is due by

MXB101
Worksheet 6
A) Questions for Group Work (compulsory)
The following 5 questions are meant to be solved in your group between Wednesday
Week 8 and Friday Week 9. Out of these 5 questions, questions 1, 2 and 4 are part
of Assignment

MXB101: Worksheet Solutions Section 1
A) Questions for Group Work (compulsory)
1.
(i)
E1 E 2 E 3 (Note if we know substance must be one of the 6, rather
than just may be, then this is E 2 E3 ).
(ii)
E1 E3 (Remember that, alternatively, the sign can always

MXB101: Worksheet Solutions Section 4
A) Questions for Group Work (compulsory)
1.
(i)
E ( X ) = ( 0 0.08 ) + (1 0.32 ) + ( 2 0.3) + (3 0.13 ) + ( 4 0.1)
+ ( 5 0.04 ) + ( 6 0.02 ) + ( 7 0.01)
= 2.1
(ii)
2
Var ( X ) = E ( X 2 ) E ( X ) with
E ( X 2 ) = ( 0

MXB101
Worksheet 5
A) Questions for Group Work (compulsory)
The following 5 questions are meant to be solved in your group between Friday Week 6
and Friday Week 7. Out of these 5 questions, questions 2, 3 and 4 are part of
Assignment 3 and question 5 is p

Solutions Worksheet Section 5
A) Questions for Group Work (compulsory)
1. Let X be the number of girls out of 10 that Bert engages in conversation with
following the use of the pick-up line. Then X ~ B(10, 0.5).
(i) 1 = 1 = 0 = 1 0.5!" = 0.999

MXB101: Solutions Section 7
A) Questions for Group Work (compulsory)
2. Let be number of times per week there is a problem with the server.
Test H! : ~ Poisson() vs H! : not Poisson()
We decide that we will reject the null hypothesis if th

MXB101
Worksheet 7
A) Questions for Group Work (compulsory)
The following 3 questions are meant to be solved in your group by Wednesday 7th May. Out of
these 3 questions, Question 1 is part of Assignment 4, which is due on Wednesday Week 10
(6th May) by c

MXB101
Worksheet 8
A) Questions for Group Work (compulsory)
The following 4 questions are meant to be solved in your group by Friday 15th
May. Out of these 4 questions, Question 3 and Question 4 are part of
Assignment 5 (in addition to the Part II of Assi

MXB101: Solutions Section 9
A) Questions for group work (compulsory)
2(i) Let ! and $ be the conviction times for manslaughter and armed robbery,
respectively.
So X ~ N(8, 52 ) and Y ~ N(6, 32) and P(! < $) = P(X Y < 0) = 0.4.
With our formulas for the ex

MXB101
WORKSHEET FOR SECTION 9
A) Questions for Group Work (compulsory)
The following 4 questions are meant to be solved in your group by Wednesday 27th May.
Out of these 4 questions, Questions 1, 2 and 4 wou

MXB101: Worksheet Solutions Section 2
A) Questions for Group Work (compulsory)
[The Group Work questions that are part of Assignment 1 will come in a separate
document.]
1. (1) P(Exactly i) = P( Ai Ai 1 )
= P( Ai ) P( Ai Ai 1 )
(due to axiom 3, as
= P( Ai

MXB101: Worksheet Solutions Section 6
A) Group Work questions (compulsory)
3. (i) Let be the number of defective fuses in 200.
Then ~ Bin(200, 0.02) with E() = 4
Use Poisson(4) to approximate Pr( = 6) 0.2149 0.1107 = 0.1042
(ii) Let be the

MXB101: Worksheet Solutions Section 8
A) Questions for Group Work (compulsory)
1. (i)
X n can take the values 0,1, 2, 3 with the probability transition matrix given
below
0.5 0.4 0.06 0.04
0.5 0.4 0.06 0.04
P=
0 0.5 0.4 0.1
0
0.5 0.5
0
(ii)
The equ