Last class review questions

# Last class review questions - Produced with a Trial Version...

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Winter2006 – selected questions Suppose X has a normal distribution with mean 3 and variance 4 and Y~N(5,9) is independent of X. Find P(2X<Y+1). A random variable X has probability function () 2 , 1 , 2 , . . . x f xx == . Find the moment generating function of X. P(A)=0.6, P(B)=0.5 and P(B¯|A)=0.5. Find P(AB). Are A and B independent? Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com

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Stat 230 Winter 2008 6. [5 Marks] MathSoc (Math Society) ties are only made by 2 companies, Pamco and Sascs and only come in 2 types, Business and Doubledeg. 60% of the ties are made by Sascs. 80% of the ties made at Sascs are Business while 70% of the Pamco ties are Business. MathSoc uses both companies to produce a box of ties for the 2009 frosh. If a particular 2009 frosh selects a tie at random from the box of ties, Fnd the probability (a) the tie has a Doubledeg style. (b) the tie came from Pamco given taht it has a Doubledeg style. 7. [11 Marks] (a) You arrive at a bus stop at 10 am knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30. i. What is the probability you will have to wait exactly 10 minutes? ii. What is the probability you will have to wait longer than 10 minutes? Page 6 of 14 Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com
Stat 230 Winter 2008 8. [19 Marks] Toxicity in water is measured in terms of EC 50. 50 represents the concentration of toxin required to kill 50% of the Fsh in a tank. Although EC50 is written as a single number, there is some ±exibility in the measurement. Essentially 2 scientists may not measure the same concentration. As a result the EC50 can be modelled using normally distributed random variables. It is known that a concentration of toxin A has an EC50 measurement distributed as A N (0 . 06 , 0 . 0025) in parts per million (ppm) and that toxin B has an

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## This note was uploaded on 10/21/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.

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