Random Variables Notes
A quantitative variable x is a random variable if the
value that it assumes, corresponding to the outcome
of an experiment is a chance or random event.
Random variables can be discrete or continuous.
Examples:
x = SAT score for a ra
Calculating Probabilities for Intersections Notes
In the previous example, we found P(A B) directly from the
table. Sometimes this is impractical or impossible. The rule for
calculating P(A B) depends on the idea of independent and
dependent events.
Two e
Descriptive and Inferential Statistics Notes
Statistics can be broken into two basic types:
Descriptive Statistics (Chapter 2):
We have already learnt this topic
Inferential Statistics (Chapters 7-13):
Methods that making decisions or predictions about a
Counting Rules Notes
Sample space of throwing 3 dice has 216 entries, sample
space of throwing 4 dice has 1296 entries,
At some point, we have to stop listing and start thinking
We need some counting rules
The mn Rule
If an experiment is performed in tw
Calculating Probabilities for Unions and Complements Notes
There are special rules that will allow you to calculate
probabilities for composite events.
The Additive Rule for Unions:
For any two events, A and B, the probability of their union,
P(A B), is
E
Event Relations Notes
The beauty of using events, rather than simple events, is that
we can combine events to make other events using logical
operations: and, or and not.
The union of two events, A and B, is the event that either A or
B or both occur when
Experiments and Events Notes
In Chapters 2, we used graphs and numerical measures to
describe data sets which were usually samples.
We measured how often using
Basic Concepts
An experiment is the process by which an observation (or
measurement) is obtaine
The Probability of an Event Notes
The probability of an event A measures how often A will
occur. We write P(A).
Suppose that an experiment is performed n times. The
relative frequency for an event A is
P(A) must be between 0 and 1.
If event A can never oc
The Multiplicative Rule for Intersections Notes
For any two events, A and B, the probability that both A and
B occur is
P(A B) = P(A) P(B given that A occurred)
=
P(A)P(B|A)
If the events A and B are independent, then the probability
that both A and B occ
The Law of Total Probability Notes
Let S1 , S2 , S3 ,., Sk be mutually exclusive and exhaustive
events (that is, one and only one must happen). Then the
probability of any event A can be written as
P(A) = P(A S1) + P(A S2) + + P(A Sk)
= P(S1)P(A|S1) + P(S
ASSIGNMENT 3
The project network is as follows:
Max numbers
Min numbers
A
4
0
16
D
3
4
20
C
5
Start
B
4
0
0
4
15
E
4
10 4
4
4
F
9
4
12
9
20
12
23
9
20
14
14
G
6
14
17
20
23
H
7
14
14
21
21
13
21
I
3
20
23
23
26
J
5
21
21
26
26
Finish
The activity time est