### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# STAT 2004, Week 9: Bernoulli and Binomial Distribution STAT 2004

Virginia Tech

GPA 3.62

### View Full Document

## About this Document

## 19

## 0

## Popular in Introductory Statistics

## Popular in Statistics

This 2 page Class Notes was uploaded by Mara DePena on Saturday March 26, 2016. The Class Notes belongs to STAT 2004 at Virginia Polytechnic Institute and State University taught by Metzger in Spring 2016. Since its upload, it has received 19 views. For similar materials see Introductory Statistics in Statistics at Virginia Polytechnic Institute and State University.

## Popular in Statistics

## Reviews for STAT 2004, Week 9: Bernoulli and Binomial Distribution

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 03/26/16

STAT 2004 WEEK 9 BERNOULLI DISTRIBUTION In a Bernoulli distribution, an outcome has two possibilities: success or failure. o Success- What we were interested in happened. o Success is represented by a 1, while failure is represented by a 0. Probability of success is represented by a p. For a Bernoulli random variable. o X ~ Bernoulli (p) o The expectation of a Bernoulli distribution = the probability of success. (E[X]=p) o Variance [X] = p (1-p) o SD [X] = the square root of the variance Categorical nominal: o You can put the number of successes and failures into a bar plot. BINOMIAL DISTRIBUTION 0 1 When you choose more than one observation from a Bernoulli distribution, that is a binomial distribution. Y ~ Binomial (n, p), with Y being a random variable, n being the number of observations and p being the probability. o E[Y]= n x p o V[Y]= n x p x (1-p) Ex: Randomly select 3 VT students. What is the probability that 2/3 are freshmen? o T ~ Binomial (3, .25) .25 is the probability and individual is a freshman, assuming the four classes are divided equally throughout the student population. o (.25) ( .75) x 3 = 14.1% The probability of a student being a freshman is raised to the number of freshmen. The probability of a student being from another class is raised to the number of students from another class. This is multiplied by the number of combinations: 3 in this case. In order to determine the number of combinations, you need a calculator. o TI-30: Type in the number of people total, click PROB, click nCr, hit enter, then type in the number you are choosing from the total number o TI-84 Type in the number of people total, click MATH, click PROB, click nCr, hit enter, then type in the number you are choosing from the total number If a question asks for the probability of “at most __ out of __,” you must calculate all three probabilities and add them together. If a questions asks for the probability of “at least __ out of ___,” you could add all the probabilities, or take the probability of the opposite. You can change a binomial distribution into a normal curve as well. o Say X ~ Binomial (50, .9) Multiple 50 and .9 together for the mean value. Then, find the variance of the binomial distribution to find the standard deviation. You now have the two values for the normal curve. N ~ (45, 2.12) You can use this to find the z-score and use your chart to find the proabability.

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.