# 410Hw05 - STAT 410 Summer 2009 Homework#5(due Friday July...

This preview shows pages 1–2. Sign up to view the full content.

STAT 410 Summer 2009 Homework #5 (due Friday, July 10, by 4:00 p.m.) 1. Let X and Y be independent random variables, each geometrically distributed with the probability of “success” p , 0 < p < 1. That is, p X ( k ) = p Y ( k ) = ( 29 1 1 - - k p p , k = 1, 2, 3, … , a) Find P ( X > Y ). [ Hint: You may find it helpful to find P ( X = Y ) first. ] b) Find P ( X + Y = n ), n = 2, 3, 4, … , and P ( X = k | X + Y = n ), k = 1, 2, 3, … , n – 1. 2. Suppose the size of largemouth bass in a particular lake is uniformly distributed over the interval 0 to 8 pounds. A fisherman catches (a random sample of) 5 fish. a) What is the probability that the smallest fish weighs less than 2 pounds? b) What is the probability that the largest fish weighs over 7 pounds? c) What is the probability that the largest fish weighs between 6 and 7 pounds? d) What is the probability that the second largest (fourth smallest) fish weighs between 4 and 6 pounds? 3. Three actuaries are independently hired to appraise the value of a company. The true value of the company is θ million dollars, and each actuary’s estimate is uniformly

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/29/2009 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.

### Page1 / 4

410Hw05 - STAT 410 Summer 2009 Homework#5(due Friday July...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online