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: