# HW12 - larger 370 You may have to look up Table 3.3 p 116...

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ECE 302, Homework #12. Due date: 4/20 http://www.ece.purdue.edu/ chihw/ECE302 07.html Prof. Chih-Chun Wang Email: [email protected] Oﬃce: MSEE354 Oﬃce Hours: MWF: 12pm–1pm TA: Kamesh Krishnamurthy, Email: [email protected] Oﬃce: POTR 370 Oﬃce Hours: M: 10–11am TTh: 10:30am–12:30pm Question 1: Suppose X 1 ,...,X n are independent random variables. Let Y = X 1 + X 2 + ··· + X n . Derive the following formula. 1. E ( Y ) = E ( X 1 ) + E ( X 2 ) + ··· + E ( X n ) 2. Var ( Y ) = n i =1 Var ( X i ) + 2 n i =1 n j = i +1 Cov ( X i ,X j ). Question 2: Problem 5.8. Question 3: Toss an unfair 6-faced dice 100 times. And suppose the probability of each face is { 2 / 7 , 1 / 7 , 1 / 7 , 1 / 7 , 1 / 7 , 1 / 7 } respectively. We can also assume that each toss is independent. Find/approximate the probability that the total sum of all 100 outcomes is
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Unformatted text preview: larger 370. You may have to look up Table 3.3 p. 116. Question 4: Problem 5.25. Question 5: Problem 5.16. Note: Designing the sample/poll size is an important subject in statistics. You want a sample size that is not too large but still gives you a suﬃciently accurate estimate, which is exactly the purpose of this problem. You should ask yourself why it is important to ﬁnd a good sample size, especially in the drug testing industry? Hint: The importance of a minimum sample/poll size can be measured in “dollars.” Question 6: Problem 5.29....
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