STAT_251_W1_2018_Assignment_2.pdf

STAT_251_W1_2018_Assignment_2.pdf - STAT 251 Assignment-2...

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Due: Monday, November 26 @ 5:00pm in STAT 251 dropbox (near ESB 1041) STAT 251 Assignment-2 Winter Term-1 2018/2019 1) a) A k-out-of-n system is one that will function if and only if at least k of the n individual components in the system function. If individual components function independently of one another, each with probability 0.9, what is the probability that a 3-out-of-5 system functions? b) Obtain where c) Service calls arrive at a maintenance center according to a Poisson process, with average 2.7 calls per minute. (i) Obtain the probability that no more than 4 calls arrive in a minute. (ii) Obtain the probability that more than 6 calls arrive in a three-minute interval 2) Let X denote the temperature at which a certain chemical reaction takes place. Suppose X has pdf Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction temperature in each lab is as given. Let Y= the number among the ten labs at which the temperature exceeds 1. What kind of distribution does Y have? Find the probability
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