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Unformatted text preview: CEE 3770 - Summer 2009 Homework 2 (due on 06/02) 1. (10 points) Suppose that X is continuous with p.d.f. f ( x ) = cx 2 , x 1. (a) Find the value of c that will make the p.d.f. integrate to 1. (b) Find the c.d.f. F ( x ) for all x . (c) Calculate E [ X ]. (d) Calculate V ar ( X ). (e) Calculate Pr (0 X 1 / 2). 2. (14 points) Jake is chosen as a semifinalist in GT Sweepstakes. This entitled him to enter the grand prize drawing for $1 million dollars. Being skeptical, Jake sat down to figure out how much money he could expect to win if he played. The prize breakdown is following: Number of winners Prize Amount 1 Grand prize $1 million 5 1st prize $1000 25 2nd prize $100 50 3rd prize $10 (a) If 250,000 people have been selected as semifinalists, how much money could Jake ap- proximately expect to win if he entered. (b) What is the variance of his possible gain? 3. (15 points) Car arriving at an intersection may either turn or go straight. The probability of turning left is 10% and the cars act independently of each other. The road has only one lane, so a left-turning car will block all cars behind it. Four cars arrive at the intersection and the light turns green....
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This note was uploaded on 06/29/2009 for the course CEE 3770 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.
- Spring '08