1
Lecture 1: Basic Concepts
ECE 514
Fundamental notions and
properties
•
What is a random experiment?
●
Randomness is associated with uncertainty,
ignorance, etc.
Ex:
1.
Take an input perfectly known to you and
apply it to a filter with a known impulse
response.
●
Don’t know the input?
L
Random?
What constitutes randomness?
2. Observe a sinusoidal wave on an oscilloscope.
Is it random?
Why?
Random Experiment
Definition
:
A random experiment
is one in which the
output cannot be perfectly known from a mere
knowledge of the input.
Properties:
❖
A random experiment is theoretically
repeatable
❖
Its output, however, cannot be predicted exactly
❑
If we cannot predict the face of a die throw, what
is the next best thing?
Example
Example
:
If we throw a coin “n” times and obtain “n
h
”
heads, what can we say about the outcome
heads?
(Assuming n goes to infinity)
n
h
/n = relative frequency
➘
If we can’t predict, exactly, what does the
frequency tell you?
Quality Assurance
1000
250
150
500
100
Tot
360
150
60
150
0
5W
200
100
0
50
50
2W
440
0
90
300
50
1W
Tot.
10K
1000
100
10
P.
Rat.
Resistor Values
Interpretation
●
Pick a resistor at random, and try to say
something about your pick.
(Remark:
same
thing when you pick a stock, using “history,”
try to “smartly” choose the right one)
•
What are the chances (probability) that you
pick a 10
W
resistor?
❖
P(10
W
) =
100/1000
= 0.1
(elementary event)
❖
P(2 W)
=
200/1000
= 0.2
●
One may want to know how likely they are at
picking a 100
W
and it be 2W.
P(10
W
, 2 W) =
50/1000= 0.05

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