Module 1
Probability
Objectives
Upon completion of this Module, students should be able to:
Use set notation (Venn diagrams) including null set, union, subset, intersection, complement, and mutually exclusive.
Explain the definitions of events, simple e

Answers to exercises in PDT module 4
WMS Exercise 5.4
a. Notice that all of the probabilities are at least 0 and they sum to 1.
b. Note F (1, 2) = P (Y1 1, Y2 2) = 1. The interpretation of this
value is that every child in the experiment either survived o

Solutions: Module 2 assessment
Question 1 [3 marks]
The mode of a discrete random variable X with probability distribution p(x)
is that value xm for which p(x) is largest (the most probable x value). Let
X Poisson().
show that the mode of the Poisson
(i)

PDT Module 2 solutions
Exercise 2.1 in Module 2 Notes
Let Y be the number of red cells in these 4 possible sub-volumes, with a probability of 0.01 of a presence
of a red cell in a sub-volume, so Y Bin(4, 0.01).
(4 )
1
Then P (Y = 1) = 1 0.01 (1 0.01)3 = 4

Module 4
Multiple random variables
Objectives
At the completion of this Module students should be able to:
Understand definitions of correlation, covariance and independence
apply the concept and definitions of joint, conditional and marginal distributi

Module 3
Continuous random variables
Objectives
Upon completion of this Module, students should be able to:
Explain the definitions of cumulative distribution function and probability
density function
Calculate the mean and variance of a continuous rand

Solutions to all exercises set in module 3 of PDT
WMS Exercise 4.11 - p167
a. We must find the value of c such that F () = f (y) dy = 1
We have
[ 2 ]2
2
4
y
=c .
F () =
cy dy = c
2 0
2
0
So, for F () = 1 we must have c 24 = 1, i.e. c =
for Y is:
cfw_ y
,

Module 1
Michael Fryer Student ID 2103767
March 16, 2016
1
Question 1
1.1
Probability of A = P(A) = probability person lived in a central city area
Therefore P(A)= number of ways event can occur divided by the total number of possible outcomes
Let CC=cent

Module 2
Discrete random variables
Objectives
Upon completion of this Module, students should be able to:
Explain the definition of a random variable
Explain the definition and usefulness of a probability distribution for a discrete
random variable
Exp

Solutions to exercises set in module 1 of PDT
WMS Exercise 2.1 - p25
Construct the three sets: A = cfw_F F ; B = cfw_M M ; C = cfw_M F, F M, M M .
Then
A B = ; A C = B C = cfw_M M C B = cfw_M F, F M
A B = cfw_F F, M M
AC =S
BC =C
WMS Exercise 2.8 - p26