Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Binomial Distribution - Lecture Notes | STAT 205, Study notes of Statistics

University of South Carolina (USC) - ColumbiaStatistics
Prof. L. Hendrix

Material Type: Notes; Professor: Hendrix; Class: ELEM STATS/BIOL&LIFE SCI; Subject: Statistics; University: University of South Carolina - Columbia; Term: Fall 2009;

Typology: Study notes

Pre 2010

Uploaded on 10/01/2009

koofers-user-es1
koofers-user-es1 ๐Ÿ‡บ๐Ÿ‡ธ

10 documents

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Binomial๎˜ƒDistribution๎˜ƒ
Letโ€™s๎˜ƒrefresh๎˜ƒour๎˜ƒmemory๎˜ƒon๎˜ƒcomputing๎˜ƒprobability๎˜ƒwith๎˜ƒan๎˜ƒexample.๎˜ƒ๎˜ƒConsider๎˜ƒthe๎˜ƒexperiment๎˜ƒ
where๎˜ƒwe๎˜ƒtoss๎˜ƒa๎˜ƒfair๎˜ƒcoin๎˜ƒ3๎˜ƒtimes.๎˜ƒ๎˜ƒFind๎˜ƒthe๎˜ƒprobability๎˜ƒdistribution๎˜ƒfor๎˜ƒflipping๎˜ƒโ€œheadsโ€๎˜ƒin๎˜ƒthis๎˜ƒ
experiment.๎˜ƒ๎˜ƒ๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
๎˜ƒ
Now,๎˜ƒthink๎˜ƒabout๎˜ƒfinding๎˜ƒprobability๎˜ƒdistributions๎˜ƒassociated๎˜ƒwith๎˜ƒflipping๎˜ƒa๎˜ƒfair๎˜ƒcoin๎˜ƒsay๎˜ƒ6๎˜ƒ
times.๎˜ƒ๎˜ƒAnd๎˜ƒthen๎˜ƒconsider๎˜ƒthe๎˜ƒexperiment๎˜ƒwhere๎˜ƒthe๎˜ƒcoin๎˜ƒis๎˜ƒnot๎˜ƒfair.๎˜ƒ๎˜ƒThe๎˜ƒcalculations๎˜ƒget๎˜ƒ
unwieldy๎˜ƒfast!๎˜ƒ๎˜ƒWe๎˜ƒneed๎˜ƒa๎˜ƒmore๎˜ƒconvenient๎˜ƒmethodโ€ฆ๎˜ƒ
pf3

Partial preview of the text

Download Binomial Distribution - Lecture Notes | STAT 205 and more Study notes Statistics in PDF only on Docsity!

Binomial Distribution

Letโ€™s refresh our memory on computing probability with an example. Consider the experiment where we toss a fair coin 3 times. Find the probability distribution for flipping โ€œheadsโ€ in this experiment. Now, think about finding probability distributions associated with flipping a fair coin say 6 times. And then consider the experiment where the coin is not fair. The calculations get unwieldy fast! We need a more convenient methodโ€ฆ

Binomial Distribution Page 2 Definition: The independent trials model occurs when (i) n independent trials are studied (ii) each trial results in a single binary observation (iii) each trialโ€™s success has (constant) probability: P{success} = p Notice that if P{success} = p, P{failure} = 1โ€“p. Your text calls this the BInS (Binary / Indep. / n is constant / Same p) setting, but is commonly referred to as a Binomial Experiment In a BInS setting, if we let Y = {# successes} then Y has a binomial distribution. NOTATION: Y ~ Bin(n,p). The binomial probability function is P{Y = j} = (^) n Cj p j (1 โ€“ p) nโ€“j j = 0,1,โ€ฆ,n where (^) n Cj = n! j!เตซnโ€jเตฏ! with j! = j(jโ€1)(jโ€2)โ€ฆ(2)(1) and define 0! = 1 Example Use the binomial probability function to find P{exactly 1 head} in the experiment where a fair coin is flipped 3 times. Find P{at least one head}