quiz5-key

# quiz5-key - r(1 − p/p 2 1 2 =[4(0.01(0.99 2 1 2 ← 4(2...

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Quiz 5. February 23, 2011 Seat # _________ Name: ___ < KEY > ___ Closed book and notes. No calculator. For Questions 1—5, consider a sequence of units coming off an assembly line. Each is defective with probability 0.01 (and otherwise not defective). Assume that different units being defective or non-defective are independent. For each question, write two answers. The first is the family of distributions of the random variable; the second is the answer to the question. 1. (2 pt) Of 100 units, the expected number of "defectives". family: ___ < binomial > ___ ____________________________________________________________ np = (100)(0.01) = 1 ____________________________________________________________ 2. (2 pt) The expected number of units until the fourth "defective" unit. family: ___ < negative binomial > ___ ____________________________________________________________ r / p = 4 / 0.01 = 400 ____________________________________________________________ 3. (2 pt) Standard deviation of the number of units until the fourth "non-defective". family: ___ < negative binomial > ___
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Unformatted text preview: ____________________________________________________________ [ r (1 − p ) /p 2 ] 1 / 2 = [4 (0.01) / (0.99) 2 ] 1 / 2 ← ____________________________________________________________ 4. (2 pt) The probability that the first "defective" is the second unit. family: ___ < geometric > ___ ____________________________________________________________ f X (2) = (1 − p ) 2 − 1 p = (0.99)(0.01) = 0.0099 ← ____________________________________________________________ 5. (2 pt) The probability that exactly one of the first ten units is "defective". family: ___ < binomial > ___ ____________________________________________________________ f X (1) = C 1 10 p 1 (1 − p ) 10 − 1 = (10) (0.01) (0.99) 9 ← ____________________________________________________________ ______________________________________________________________________ Write on the back any concerns about the weekly quizzes or the course in general. IE 230 – Page 1 of 1 – Schmeiser...
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## This note was uploaded on 04/25/2011 for the course IE 230 taught by Professor Xangi during the Spring '08 term at Purdue.

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