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Stat 330 (Spring 2015): Homework 4 Due: February 16, 2015 Show all of your work, and please staple your assignment if you use more than one sheet. Write your name, the course number and the section on every sheet. Problems marked with * will be graded and one additional randomly chosen problem will be graded. 1. * When circuit boards used in the manufacture of portable disk drives are tested, the long-run percentage of defectives is 5%. Assume that the events that the boards are defective or not occur independently of each other. (a) Calculate the probability of finding exactly 3 defective circuit boards in a batch of twenty five. (b) Calculate the probability of finding at most 3 defective circuit boards in a batch of twenty five. (c) Calculate the probability of finding more than 1 but less than 4 defective circuit boards in a batch of twenty five. (d) Calculate the probability that at least 5 circuit boards have to be tested before a defective circuit board is found. 2. A digital communication channel has an error rate of 10−7 , which may be taken to mean that the probability of any bit (a one or a zero) arriving incorrectly at the destination is 10−7 . What is the probability that a transmission of a million bits occurs without a single error? It is reasonable to assume that the transmission of a given bit (incorrectly or correctly) does not affect the transmission of other bits. State clearly the random variable and the probability distribution you are using and the values of the parameters associated with that distribution. 3. (Baron’s book): 3.1 4. * (Baron’s book): 3.18 5. (Baron’s book): 3.23 1