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AP Stats - Chapter 17

Page history last edited by Mrs. Gallagher 16 years ago

 

Chapter 17: Probability Models

 

 

Key Vocabulary:

Bernoulli trials- There are only 2 possible outcomes(success or failure), the probability of success is the same on each trial, and the trials are

independent.

Geometric model- shows how long it takes to achieve a success.

Binomial model- requires two parameters, Binom(n,p)

Calculator Skills:

geometpdf( found under 2nd Dist, used to find the probability that it takes a certain number of trials to get a success.  When using, you put in geometpdf(probability, # of trials)

geometcdf(cumulative density function, finds the sum of the probabilities of several possible outcomes. calculates the the probability of finding the first success on or before the xth trial....

binompdf(- located under 2nd Dist and allows us to find the probability of an individual outcome.  Known as binompdf(n,p,k), where n stands for number of trials, p stands for probability of success, and k is the desired number of successes.

binomcdf(-located under 2nd Dist and allows us to find the total probability of getting x or fewer successes among n trails.  Known as

binomcdf(n,p,X), n stands for number of trials, p stands for probabilty, and X stands for number of successes from x number to 0.

 

 

 

1. List three characteristics of Bernoulli trials.

1.) There are only 2 possible outcomes on each trial

2.) The probability of success is the same on every trial

3.) The trials are independent

 

2. What is the variable of interest in a geometric model?

 

The variable of interest in a geometric model is how long it will take to achieve success. (i.e., the Step by Step problem, How long will it take them to find someone with O negative blood?)

 

[see box on bottom of 326 for important formulas]

 

3. How do you find the expected value and standard deviation of a geometric random variable?

 

      expected value : mean = 1/p , where p = the probability of success

      standard deviation = square root(q/(p squared))  where q = probability of failure

 

4. In the geometic distribution, what does the parameter p represent?

 

p represents the probablity of success (q = 1 - p is probability of failure)

 

5. If X has a geometric distribution, what does (1 – p)n – 1p represent?

 

6. What is the difference between a probability distribution function (pdf) and a cumulative distribution function (cdf)?

 

A probablility distribution function finds the probability of any individual outcome. A cumulative distribution function finds the sum of the probabilities of several possible outcomes.

 

7. What is the variable of interest in a binomial model?

the variable of interest is the number of successes

 

8. Explain the difference between the binomial setting and the geometric setting.

 

 A geometric setting is used to see how long it will take to achieve a success. The geometric setting has one parameter, the probability of success.

 

A binomial setting is used to measure the number of successes. Binomial setting has two parameters, number of trials and probability of success.

 

9. How do you find the expected value and standard deviation of a binomial random variable?

 

expected value=np SD= suare root of npq

 

10. In the binomial distribution, what do parameters n and p represent?

The number of trials n, and the probability of success p.

 

11. What is meant by B(n, p) ?

 

Binomial Model.   Binom(n(number of trials),p(probability of success))

 

12. In the formula nCk , what does n represent? What does k represent?

 

The n represents trials and k represents successes

 

What does the value of represent?

13. Complete the following table of values:

 

1! 1 1

2! 2 x 1 2

3! 3 x 2 x 1 6

4! 4 x 3 x 2 x 1 24

 

5! 5 x 4 x 3 x 2 x 1

6! 6 x 5 x 4 x 3 x 2 x 1 144

7! 7 x 6 x 5 x 4 x 3 x 2 x 1 1008

n! n x n-1 x n-2 x n-3...  

 

 

14. What is the value of ?

 

 

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