### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Statistics for Research I STAT 537

UT

GPA 3.94

### View Full Document

## 23

## 0

## Popular in Course

## Popular in Statistics

This 16 page Class Notes was uploaded by Kamren McLaughlin on Monday October 26, 2015. The Class Notes belongs to STAT 537 at University of Tennessee - Knoxville taught by James Schmidhammer in Fall. Since its upload, it has received 23 views. For similar materials see /class/229891/stat-537-university-of-tennessee-knoxville in Statistics at University of Tennessee - Knoxville.

## Reviews for Statistics for Research I

### 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: 10/26/15

Continuous Random Variables M3 of a continuous random variable Consider an experiment having an in nite number of possible outcomes Assign some real number to each possible outcome and associate this number with some random variable say X Example Weighing jellybeans Imagine purchasing a bag of 100 jelly beans and weighing each bean on a scale that is very accurate and very precise X weight of jellybean Def 3 of the probability density function of a continuous random variable X Let X be a continuous random variable assuming all values in some range Rx of the real line Then the probability density function of X is that function fX such that Pa g X g b fxdx Properties of f x l fx20 for allx lt2 jfltxgtdx1 Def 3 Mean of a continuous random variable X H EX jxfltxgtdx Def 3 Variance of a continuous random variable X 52 VarX EX 2 Zoe u2fxdx Def 3 Standard Deviation of random variable X 62 Def 3 Skewness of a continuous random variable X H3 Ix u3fxdx Def 3 Kurtosis of a continuous random variable X H4 Jx u4fxdx Def 3 Cumulative Distribution Function of a continuous random variable X Fx PX g x fooow The Normal Distribution M3 The normal d 3 A continuous random variable X is said to have a normal distribution with parameters u and 62 00 lt u lt oojcs2 gt 0 if the probability density function of X is 1 1xiH2 3 2 e G wltxltw V2756 Notation X Nu62 fx Moments Mean EX u Variance VarX 62 H2 Skewness u3zO gtBI 330 62 H4 Kurtos1s BZ 3 gtBZ O 4 G Normal Distribution p Sc p Zc u c p 6 26 36 Def 3 The standard normal d LL20 621 1 71x2 fx2e2 ooltxltoo TE Notation X NO1 Property If XNn62 and ifz X then 2 NO 1 The Standard Normal Distribution Standard Normal Distribution Pzgt17504006 Standard Normal Distribution 95994 0400 2 z175 Pzgt2370089 Standard Normal Distribution 9911 0089 4 3 2 1 o 1 2 2237 3 Reproductive Property Let c1x2xn be 11 independent normally distributed random variables with X Nuxics Let y ZaiXl i1 Then y N Hy i where My Zaiuxi i1 Central Limit Th m LindbergLevy Let c1x2xn be 11 iid random variables with EltXigtultoo VarXi 62 0 lt62 ltoo Let 1 n X XZ n 11 so that Y 2 H C32 63 11 Let Y X Hf X H Ti TN Then Y gtNO1 as n gtoo Application Normal Approximation to Binomial D Let X1Xn be iid Bernoulli random Variables so that Y 2 Zn X1 Binomial n p H with EY Hy quot9 VarY oi 71191 P Then Y Zz HyzY np gtNO1 as n gtoo 6y an 19 Rule of Thumb Normal Approximation to binomial is good if minnp nq 2 5 Example X Binomial n5 p04 3496 2592 2304 0778 0768 0102 3496 3 2592 2304 2 1 0778 0768 l 0102 For X Binomialn 519 04 M quotI 2 6inp1 p12 Using the exact binomial distribution Oquot quotOUOquot39U PX 1 00778 02592 2 03370 PXlt 1 Exact Probability 040 O 33 033 025 020 015 010 OCE Using normal approximation X np 1 2 PX 1P anG p 12 PZ 3 0913 01806 not so good PXlt 1 Normal Approxima on 040 O 33 033 OquotquotquotOUOquot39U

### 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

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "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!"

#### "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.