1. ECEN4503 Random Signals Week 4 Dr. George Scheets
Read , 4.6
Problems 4.23, 35 – 37, 89 – 91
Quiz #2 Results Hi = 10, Low = 0.7, Ave = 5.80, σ = Quiz 2B scores bumped by +1

2. Examples of Gaussian Noise
Radio Static (Thermal Noise)
Analog TV "snow"
2 seconds
of White Noise

3. Unconditional PDF X ≡ Clearance
P( 0.01 < X < 0.02) = # favorable outcomes
# of outcomes
= 56/8000 =
We can do
this for every
bin. Result
should ∑ = 1.

4. Conditional PDF Suppose we remove all devices (103 of them)
with clearance < 0.01 inches.
7,897 devices remain.

5. Conditional PDF X ≡ Clearance
P( 0.01 < X < 0.02 | X > 0.01) =
# favorable outcomes = 56/7897 =
# of outcomes
We can do
this for every
bin. Result
should ∑ = 1.

6. To find a Conditional PDF...
Start with unconditional PDF fX(x).
Throw out region not needed
Normalize remaining area. -∞ +∞ ∫
fX(x)dx = 0.85?

7. To find a Conditional PDF...
Start with unconditional PDF fX(x).
Throw out region not needed
Normalize remaining area. -∞ +∞ ∫
[fX(x)/0.85]dx = 1.0
[Bracketed term] is the
conditional PDF fX(x | ??).

8. ∫ ∑ Expected Values E[ * ] = (*) fX(x) dx-∞ +∞ ∫
E[ * ] = (*) fX(x) dx
E[ * ] = (*i)P(*i) (discrete) ∑
all possible
outcomes

9. Standard Deviation Square root of average squared deviation from the mean.
Example: X = {6, 8, 10} Average = (6+8+10)/3 = 8 Average |Deviation| from the mean = ( )/3 = 4/3 = 1.333
Average squared deviation from the mean = ( )/3 = 8/3 = Standard Deviation = = 1.633

10. Random Signals Trivia
"In the United States, HIV is transmitted from an infected mother to her infant about 30% of the time. At least 6,000 HIV infected women given birth in the United States each year, and therefore a minimum of 1,800 children become infected in a year's time." Science, 17 July 1992

11. 70%
"Share of students who consider themselves above average in mathematical ability- a mathematical impossibility." "In Praise of the Ordinary Child" Time Magazine, 3 August 2015

12. Neb. lottery draws same numbers twice in row
Neb. lottery draws same numbers twice in row. The odds of such an odd occurrence? One in a million
"Lottery spokesman Brian Rockey says one of two lottery computers that randomly generate combinations picked the numbers 1, 9 and 6 — in that order — for Monday night's drawing. He says the other computer picked the same three numbers Tuesday in the same sequence."
-Associated Press, 22 Jan 2009

13. Let's Make a Deal
3 Doors Behind 2 doors is a decent prize Behind 1 door is a fabulous prize
Contestant picks a door (not opened)
Host opens a door with a decent prize
Does not open door picked by contestant
Contestant has option of switching doors Gets whatever is behind picked door

14. Your Money or Your Life Behind 2 doors Mafia hit man with a shotgun
Behind 1 door is $1,000,000,000

15. Your Money or Your Life 1 2 3
Suppose you pick door number 3

16. Your Money or Your Life 2 3
From a probability viewpoint, what tactic will maximize your chance of winning?
Stay with door originally chosen
Change doors
Mentally flip a coin.
It doesn't matter, the odds are same for all above.

17. Your Money or Your Life 2
From a probability viewpoint, what tactic will maximize your chance of winning?
Stay with door originally chosen
Change doors
Mentally flip a coin.
It doesn't matter, the odds are the same.

18. Strategy... Stay with door originally chosen Change doors
You must pick correct door initially 33% chance of winning.
Change doors
You win if you initially pick wrong door 67% chance of winning.
Mentally flip a coin after 1 door is opened
You have a 50% chance of winning.
It doesn't matter, the odds are the same
It matters.

19. Lottery Assistance