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: Providenci Mosciski Sr.


Providenci Mosciski Sr.
GPA 3.66


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

Class Notes
25 ?




Popular in Course

Popular in Statistics

This 2 page Class Notes was uploaded by Providenci Mosciski Sr. on Wednesday September 9, 2015. The Class Notes belongs to STAT 394 at University of Washington taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/192514/stat-394-university-of-washington in Statistics at University of Washington.




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: 09/09/15
Lecture 28 More functions of continuous random variables 281 The log of a Uniform random variable Suppose X is Uniform 01 and let Y 710g X Note 0 lt X lt 1 so 0 lt Y lt oo Fyy PY y P10gX y 1310ng 7y 7 P X 7 1 1d 1 7 gtex 7 7 78X 7 7 p 24 AXPH p 24 WW Pity 7 expky 0ltyltltgt0 That is Y is an exponential random variable with parameter 1 282 Maxima and minima of independent random variables a Suppose X1 X2 are independent and have cdf F1m F2m Let Y maxlgign Xi 130 S y Pall the X are g y TL PXy 7 HEW i1 H 13 H because the X are independent b Now with the same Xi let W mlnlgign 17 PY gt y Pall the X are gt y V L V L HPOQ gt y H1Fz y i1 13971 283 The Max of uniform random variables Suppose X are independent and all are Uniform 01 rvs Let Y maxlgign Xi Then z and Fyz PY z z Note that as n 7 00 m 7 O Y piles up the probability closer and closer to 1 So instead let us consider V n17 Y PV U Pl 7 Y vn PY 217 vn 17Fy1 71171 17 1 7 3 7gt17exp7v 71 That is fvv exp7v V is exponential with parameter 1 284 The Minimum of exponential random variables Suppose Xa X5 and X0 are independent exponential rvs with rates Au b and Ac Let Y minXa X5 X0 For example X are waiting times for busses a is No 48 b is No72 c is No 373 17 PY gt y Pall the X are gt y PXa gt yPXb gt yPXc gt 00 00 Now PXa gt y may Aaexp7xazdz 7 exp7az exp7ay y 2 SO 1 Fifty expayexpbyexpcy expa b My My FHy A A1 Acexp7Aa A1 My That is Y is an exponential random variable with rate parameter a b Ac This makes sense if I can take any of the three busses collectively they arrive at the sum of the rates and my expected waiting time is 1rate Lectures 293031 REVIEW Review of conditional probability Midterm 2 question 1 Review of Bernoulli process Midterm 27 question 3 Another Bernoulli process example Homework 87 Ch 37 No79 Other examples 7 ask Crib sheet for nal7 essentially as for midterm 2 Plus a Normal probability table will be provided


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

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!"

Anthony Lee UC Santa Barbara

"I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

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."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

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.