New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

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

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here


by: Darien Kutch


Marketplace > Texas A&M University > Statistics > STAT 211 > PRIN OF STATISTICS I
Darien Kutch
Texas A&M
GPA 3.54

Samiran Sinha

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Samiran Sinha
Class Notes
25 ?




Popular in Course

Popular in Statistics

This 4 page Class Notes was uploaded by Darien Kutch on Wednesday October 21, 2015. The Class Notes belongs to STAT 211 at Texas A&M University taught by Samiran Sinha in Fall. Since its upload, it has received 35 views. For similar materials see /class/225750/stat-211-texas-a-m-university in Statistics at Texas A&M University.

Similar to STAT 211 at Texas A&M




Report this Material


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: 10/21/15
Crib Sheet for Exam 2 Statistics 211 1 Chapter 5 Joint Probability Distributions Marginal probability massdensity function we 72pm pyltygt72pltmgt mac 7 mm my mm Y X 700 700 TWO RV X Y are independent if for every pair of X Y 1017 9 PX I Pyy ay 121 My otherwise they are dependent Conditional probability density function of Y given that X z is ay fyix f 7 00 lt y lt oo pY X May 1 I Expected values Ewangt1Zmepm Emmigt17 m mhltzygtfltzygtdzdy Gamay 7 EX 7 my 7 m 7 Em 7 My may COTTXY w 71S pg S 1 aXaY Central Limit Theorem CLT states that if our random variables X have a dis tribution With Whose mean and variance exist and X1 X2 Xn are a random sample and our sample is large say n 2 30 then 2 7 a X N 1W7 2 Linear combinations Ea1X1 aan a1EX1 anEXn Va1X1 aan ZZaiajC0vXZ Xj i1 j1 lf X1 Xn are mutually independent then Va1X1 aan a VX1 ailan since C0vXZXj 0 When ia j and C0vXZXi VXi lf X1 Xn are independent and normal though they may have different M and al for each Xi then any linear combination of X s also has a normal distribution 2 Chapter 7 Confidence Intervals Basic con dence interval7 a is known 7 a z i Zed2W Large sample Cl 7 s z i Zed2W Cl for p if n13 2 5 and m 2 5 and n is small compared to the population size N 5 i Z042 lln A small sample Cl 3 i i tut27171 l i i tut27L71 8H1 TL n7 1 n7 1 J 2 7 2 XaQmil Mia27171 Prediction interval Cl for 02 Sample size calculations a 2 4Z2 t n lt2Za2Zgt n L22 3 Chapter 8 One Sample Hypothesis Tests One Sample test for mean 7 Normal distribution amp a is known i i 0 Z a Alternative hypothesis Rejection region for level a test Ha M gt 0 Z 2 Z0 Ha I M lt 0 Z S 7Z0 Hail flio ZZZa2 0r ZS Za2 Type ll Error Formulas for 50 Alternative hypothesis Type ll error for size a test H 7M HaAMgtMo ltIgtlt2aU N gt H 7M Hazlt0 li lt7za a gt HaMH Mo at gm i a wt2 m Sample sizes and Type ll errors Alternative hypothesis Sample size Hazwm HaiMiMo Wf One Sample Test for Mean 7 Large Sample CLT iiiL0 Z s Rejection region is the same as one sample Ztest abovei One sample test for mean 7 Normal distribution amp a is unknown film 5N5 Alternative hypothesis Rejection region for level a test Ha M gt 0 75275057171 Ha M lt 0 75S 45047171 Ha 1 i 0 752 tut27L71 OF 75S itaQmil Large sample tests concerning a population proportion p Alternative hypothesis a I p gt p0 Ha I P lt P0 Ha P Po P PO P0 0n Rejection region for level a test Z gt Z Z E 720 Z 2 Z042 or Z S Za2 Note that npo 2 5 and ram 2 5 for this test to hold Type ll error formulas for Bp Alternative hypothesis Ha I P gt P0 Ha I P lt P0 HarPy Po Type ll error for size a test PeepZMpoqon PWn 17 i PoiPizaxPoqongt PHIM ltPoiPZa2P0110n xPqhl 7 PeepZazlfpoqon xPqM Sample sizes and Type ll errors Alternative hypothesis Sample size Ha I gt P0 JAN t pull 2 Ha I lt P0 MM t pull 2 Ha p p0 2 The pValue for a Z test is calculated as follows 17 ltIgtZ for an uppertailed test for a lowertailed test 2l 7 for a twotailed test pValue


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

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

Jim McGreen Ohio University

"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."

Amaris Trozzo George Washington University

"I made $350 in just two days after posting my first study guide."

Bentley McCaw University of Florida

"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!"

Parker Thompson 500 Startups

"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."

Become an Elite Notetaker and start selling your notes online!

Refund 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


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:

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

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.