Standard Deviation and Variance Essay

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POD #4

1/10/2012

Deal?

Golden Road Game


Video

POD #5
1/11/2012
MC
#9
It is Wednesday once again…. Time for our weekly MC practice! 
Remember to use your resources – talk it through with your partners, use your notebook, but really try each problem! You don’t get better by just watching others work problems 

Stats: Modeling the
World
Chapter 16
Random Variables

Random Variables
A random variable assumes any of several different values as a result of some random event.
Discrete random variables can take one of a finite number of distinct outcomes.


Example: Number of credit hours

Continuous random variables can take any numeric value within a range of values.


Example: Length of your desk

Let’s check…
Discrete or Continuous?


The number of desks in a classroom.
Discrete





The fuel efficiency (mpg) of an automobile.
Continuous
The distance that a person throws a baseball.



Continuous
The number of questions asked during a statistics exam.
Discrete

From Yesterday’s Lab…
The probability model for a random variable consists of:
-the collection of all the possible values and
-the probability that they occur
Mean/Expected Value

Variance & Standard Dev

E ( x )    x  P ( x )

Var ( X )  ( x   )  P ( x )
2

SD ( X )  variance

Expected Winnings?
A club sells raffle tickets for $5. There are 10 prizes of $25 and 1 grand prize of $100. If 200 tickets are sold…
Create the probability model:

Prize

25

100

Prob

10/200

1/200

0
189/200

Can you figure out how much you can expect to win?
 10 
 1   189 
E (x ) 25
  100
  0
  1.75
 200 
 200   200 
With what variance?

 10 
2 1  var( x ) ( 25  1.75) 
  (100  1.75) 
  ... 
 200 
 200 
2

78.1875

Example
A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.)
a) Make a list of all possible children combinations they could have.

G, BG, BBG, BBB
b) Create a probability model for the number of children they’ll have.
# of kids
Probability

1
.50

2

3

.25

.25

b) How many children can this family expect to have?

E (x ) 1 0.50   2 0.25  3 0.25 

1.75

Example
The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.
Repair calls
0
1
2
3
Probability
0.1
0.3
0.4
0.2
a) How many calls should the shop expect per hour?

E (x ) 0 0.1  1 0.3  2 0.4   3 0.2   1.7
b) What is the variance and standard deviation?

var( x ) (0  1.7) 2 (0.1)  ...  (3  1.7) 2 (0.2)  0.81

stdev ( x )  0.81 0.9

POD #6
Deal/No Deal

1/12/2012

Linear Transformation Rules

Flashback!!!
Recall…
- Adding or subtracting a constant changes the MEAN, but NOT the SPREAD (standard deviation or variance)
For random variables, that means:

E(X ± c) = E(X) ± c

Var(X ± c) = Var(X)

Another Flashback!!!
Recall…
- Multiplying by a constant changes BOTH the MEAN
AND the SPREAD (standard deviation or variance)
Note: Since Variance is a squared term, it will change by the constant squared
For random variables, that means:

E(aX) = aE(X)

Var(aX) = a Var(X)
2

POD #7
FRQ

1/13/2012

AP

It’s Friday!!!
You have 15 minutes to answer the AP Free
Response question to the best of your ability.
Remember – NO BLANKS!! ALWAYS TRY!! 
Afterwards, you will need yesterday’s worksheet, calculator, paper, and pencil

Combining Random Variables

Combining Random Variables
Means:
When adding two random variables (X and Y), the mean of the total = _________________________
When subtracting two random variables (X and Y), the mean of the differences = ________________
E(X ± Y) = E(X) ± E(Y)

Combining Random Variables
Variances:
When adding two INDEPENDENT random variables (X and Y), the variance of the total = ________________
When subtracting two INDEPENDENT random variables (X and Y), the variance of the difference =
______________
NOTE:
Show More

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