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# ps04 - University of Illinois Spring 2010 ECE 313 Problem...

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University of Illinois Spring 2010 ECE 313: Problem Set 4 Counting Random Variables, Maximum-Likelihood Estimation Due: Wednesday February 17 at 4 p.m. Reading: Ross Chapter 4. Noncredit Exercises: Chap. 4: Problems 32, 38-39, 40-43, 47-52; Theoretical Exercises 10, 11, 13-20, Self-test problems 11-14 1. [The Binomial Random Variable I] Consider a football game in where the offense has 5 offensive linemen lined up at the line of scrimmage. An offensive lineman will move before the ball is snapped - resulting in a false start - independently of any other lineman with probability 10 - 3 . (a) Specify the probability of a false start, p fs on any offensive play (b) Suppose a typical football game has 100 offensive snaps in a game. Specify the pmf for the random variable X denoting the number of false starts in the game. (c) A false start results in loss of 5 yards on any play. What is the expected amount of total yards in penalty incurred during a game? 2. [Geometric Random Variables] During a bad economy, a graduating ECE student goes to career fair booths in the technology sector (e.g. Google, Apple, Qualcomm, Texas Instruments, Motorola, etc) - and his/her likelihood of receiving an interview request after a career fair booth visit depends on how well he/she did in ECE 313. Specifically, an A in 313 results in a probability p A = 0 . 95 of an interview, whereas a C in 313 results in a probability of p B = 0 . 15 of an interview. (a) Give the pmf for the random variable Y that denotes the number of career fair booth visits a student must make before his/her first interview invitation. (b) On average, how many booth visits must an A student make before getting an interview, as compared to a C student? (c) Suppose that during a typical career fair, there are a total of 5 booth visits that can be made in the technology sector. Find the minimum value of p for which a student can expect to get an interview in his/her senior year. What does this mean, on average, about the C student in 313?

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