DOC PREVIEW
UNC-Chapel Hill STOR 155 - Lecture 12 - Birthday Problem, Prisoner Dilemma, Random Variable

This preview shows page 1-2-20-21 out of 21 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

10/13/09 Lecture 12 1STOR 155 Introductory StatisticsLecture 12: Birthday Problem, Prisoner Dilemma, Random VariableThe UNIVERSITY of NORTH CAROLINAat CHAPEL HILL10/13/09 Lecture 12 2Review10/13/09 Lecture 12 310/13/09 Lecture 12 410/13/09 Lecture 12 510/13/09 Lecture 12 6Birthday Problem• In a classroom of 45 people, what is the probability that at least two people have the same birthday?• Event A: at least two people have the same birthday out of the 45 people.• AC: every person has a different birthday out of the 45 people. • P(A) = 1 - P(AC) = … (see the board)10/13/09 Lecture 12 73 Prisoners’ Dilemma• Three prisoners A, B and C are on a death row. The governor decides to pardon one of the three and chooses at random the prisoner to pardon. • He informs the warden of his choice but requests that the name be kept secret for a few days.• The next day, A tries to get the warden to tell him who had been pardoned.• The warden refuses. A then asks which of B or C will be executed. The warden thinks for a while, then tells A that B is to be executed.10/13/09 Lecture 12 83 Prisoners’ DilemmaA's reaction: Given that B will be executed, then either A or C will be pardoned, my chance of being pardoned has increased from 1/3 to 1/2.Q: Is A correct ? Did the warden disclose any information to A ? Can A increase his chance of survival by swapping with C ?10/13/09 Lecture 12 9Free throws• A TarHeel basketball player is a 80% free throw shooter.• Suppose he will shoot 20 free throws during each practice.• Which is more likely: to make 5 out of 20, or 18 out of 20 ?• How many free throws he makes on average during practice?10/13/09 Lecture 12 10• Experiment: – A TarHeel basketball player shoots 20 free throws during his practice.– X: number of hits• A random variable is a variable whose value is a numerical outcome of a random experiment. Random Variables10/13/09 Lecture 12 11Two types of random variables• A discrete random variable has a finitenumber of possible values. – X: number of hits when trying 20 free throws.– Possible values for X: 0,1, …, 20• A continuous random variable takes values in an interval.– X: the time it takes for a bulb to burn out.– Possible values are not countable.10/13/09 Lecture 12 12Discrete Random Variable10/13/09 Lecture 12 13Flip a coin 4 times• Find the probability distribution of the random variable describing the number of heads that turn up when a fair coin is flipped 4 times.• Solution1/164/166/164/161/1610/13/09 Lecture 12 14Probability Histogram10/13/09 Lecture 12 15Questions• What is the connection with histograms we talked about in Chapter 1?• Are the two problems similar (toss a coin 4 times and shoot 20 free throws) ? Yes or no … the ``free throw’’ problem is equivalent to tossing a biased coin 20 times, each with P(H) = 0.8.10/13/09 Lecture 12 16Continuous Random Variable (spinner)10/13/09 Lecture 12 17Continuous Random Variable• A continuous random variable X takes all possible values in an interval.– Not countable• The probability distribution of a continuous r.v. Xis described by a density curve. – What is a density curve?10/13/09 Lecture 12 18Ex: Spinner (continued)• P( point to 1/4) = 0 (why ?)• P( greater than 5/8) = 1 – 5/8 = 3/8• P( between 2/9 and 7/8) = 7/8 – 2/9 = …• P( falling in (x, x+1/4)) = 1/4 for any x greater than 0 and less than 3/4.10/13/09 Lecture 12 19Continuous Distribution• The probability of any event is the area under the density curve and above the values of X that make up the event.10/13/09 Lecture 12 20Continuous Distribution• The probability model for a continuous random variable assigns probabilities to intervals of outcomes rather than to individual outcomes.• In fact, all continuous probability distributions assign probability 0 to every individual outcome.– The spinner• Normal distributions are continuous probability distributions.10/13/09 Lecture 12 21Women Height• The height of American women aged 18 – 24 is approximately normally distributed with mean 64.3 inches and s.d. 2.4 inches. Two women in the age group are randomly selected. • What is the probability that both of them are taller than 66


View Full Document

UNC-Chapel Hill STOR 155 - Lecture 12 - Birthday Problem, Prisoner Dilemma, Random Variable

Documents in this Course
Exam 1

Exam 1

2 pages

Load more
Download Lecture 12 - Birthday Problem, Prisoner Dilemma, Random Variable
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture 12 - Birthday Problem, Prisoner Dilemma, Random Variable and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture 12 - Birthday Problem, Prisoner Dilemma, Random Variable 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?