Mathematics > QUESTIONS & ANSWERS > University of California, Berkeley - CS 70 dis13a CS 70 Discrete Mathematics and Probability Theory (All)

University of California, Berkeley - CS 70 dis13a CS 70 Discrete Mathematics and Probability Theory Spring 2017- All Solutions Worked.

Document Content and Description Below

CS 70 Discrete Mathematics and Probability Theory Spring 2017 Rao DIS 13a 1 Uniform Means Let X1;X2;:::;Xn be n independent and identically distributed uniform random variables on the interval ... [0;1]. (a) Let Y = minfX1;X2;:::;Xng. Find E(Y). [Hint: Use the tail sum formula, which says the expected value of a nonnegative random variable is E(X) = R0¥ Pr(X > x)dx. Note that we can use the tail sum formula since Y ≥ 0.] (b) Let Z = maxfX1;X2;:::;Xng. Find E(Z). [Hint: Find the CDF.] 2 Conditioning on Exponentials Let Xi be i.i.d. Expo(l) random variables. (a) Compute E[Y j Z], where Y = maxfX1;X2g and Z = minfX1;X2g. (b) Compute E[X1 +X2 j Z]. [Hint: Use part (a).] (c) Use part (b) to compute E[Z]. (d) Compute E[X1 +X2 j X1 +X2 +X3]. CS 70, Spring 2017, DIS 13a 3 3 Bayesian Darts You play a game of darts with your friend. You are better than he is, and the distances of your darts to the center of the target are i.i.d. U[0;1] whereas his are i.i.d. U[0;2]. To make the game fair, you agree that you will throw one dart and he will throw two darts. The dart closest to the center wins the game. What is the probability that you will win? Note: The distances from the center of the board are uniform. [Show More]

Last updated: 1 year ago

Preview 1 out of 5 pages

Add to cart

Instant download

document-preview

Buy this document to get the full access instantly

Instant Download Access after purchase

Add to cart

Instant download

Reviews( 0 )

$12.00

Add to cart

Instant download

Can't find what you want? Try our AI powered Search

OR

REQUEST DOCUMENT
40
0

Document information


Connected school, study & course


About the document


Uploaded On

Apr 16, 2021

Number of pages

5

Written in

Seller


seller-icon
Kirsch

Member since 4 years

905 Documents Sold


Additional information

This document has been written for:

Uploaded

Apr 16, 2021

Downloads

 0

Views

 40

Document Keyword Tags


$12.00
What is Browsegrades

In Browsegrades, a student can earn by offering help to other student. Students can help other students with materials by upploading their notes and earn money.

We are here to help

We're available through e-mail, Twitter, Facebook, and live chat.
 FAQ
 Questions? Leave a message!

Follow us on
 Twitter

Copyright © Browsegrades · High quality services·