report
loard123
week03.ppt3-1 Introduction
- Experiment
- Random
- Random experiment
3-1 Introduction
3-1 Introduction
3-1 Introduction
3-1 Introduction
3-2 Random Variables
- In an experiment, a measurement is usually
denoted by a variable such as X.
- In a random experiment, a variable whose
measured value can change (from one replicate of
the experiment to another) is referred to as a
random variable.
3-2 Random Variables
3-3 Probability
- Used to quantify likelihood or chance
- Used to represent risk or uncertainty in engineering
applications
- Can be interpreted as our degree of belief or
relative frequency
3-3 Probability
- Probability statements describe the likelihood that
particular values occur.
- The likelihood is quantified by assigning a number
from the interval [0, 1] to the set of values (or a
percentage from 0 to 100%).
- Higher numbers indicate that the set of values is
more likely.
3-3 Probability
- A probability is usually expressed in terms of a
random variable.
- For the part length example, X denotes the part
length and the probability statement can be written
in either of the following forms
- Both equations state that the probability that the
random variable X assumes a value in [10.8, 11.2] is
0.25.
3-3 Probability
Complement of an Event
- Given a set E, the complement of E is the set of
elements that are not in E. The complement is
denoted as E’.
Mutually Exclusive Events
- The sets E1 , E2 ,...,Ek are mutually exclusive if the
intersection of any pair is empty. That is, each
element is in one and only one of the sets E1 , E2
,...,Ek .
3-3 Probability
Probability Properties
3-3 Probability
Events
- A measured value is not always obtained from an
experiment. Sometimes, the result is only classified
(into one of several possible categories).
- These categories are often referred to as events.
Illustrations
- The current measurement might only be
recorded as low, medium, or high; a manufactured
electronic component might be classified only as
defective or not; and either a message is sent through a
network or not.
