ST235: Probability
Problems Sheet 2 : Probability Rules
1. Suppose A and B are mutually exclusive events for which P (A) = 0.3 and P (B) = 0.5.
What is the probability that
(a)
(b)
(c)
(d)
(e)
either A or B occurs;
A occurs but B does not;
both A and B oc
ST235: Probability
Problems Sheet 4 Transformations of Random Variables,
Expectation & Moment Generating Functions
1. If X is uniformly distributed over (0,1), find the probability density function of Y = eX .
2. If X has a uniform distribution U (/2, /2)
ST235: Probability
Problems Sheet 1 : Counting
1. How many different letter arrangements can be made from the words
(a) democrat;
(b) propose;
(c) mississippi?
2. In how many ways can 8 people be seated in a row if
(a) there are no restrictions on the sea
ST235: Probability
Problems Sheet 3 Random Variables
1. A certain historical document is known to have been written by either author A or author
B. Until now, it was thought equally likely to have been written by either author. Further
evidence of authors
Chapter 2
Introduction to Probability
2.1
2.1.1
Sample spaces, events and sets
Introduction
Probability is the language we use to model uncertainty. The data and examples we looked at in the
last chapter were the outcomes of scientific experiments. Howeve
Probability
Bottling Plant
A bottling plant has 3 machines A1 , A2 , and A3 with production split as
follows:
A1 provides 50% of production
A2 provides 30% of production
A3 provides 20% of production
A problem in the bottling process is improper sealing a
MA235: 1
Prussian Cavalry Ocer Deaths
Deaths of Prussian cavalry ocers from
horsekicks.
Data from 10 corps for 20 years.
Deaths
No of
Years
0
1
2
3
4
>5
109
65
22
3
1
0
Total
200
Slide 1
Flying Bomb Hits on South London
Area divided into 576
1
4
km2 areas
08/09/2016
1. Coun(ng
1.1 Fundamental Theorem
If a job consists of k separate tasks, the ith of
which can be done in ni ways, i=1,2,k, then
the enAre job can be done in
n1 x n2 x x nk ways
Counting: how to solve it!
Try simple case small numbe