# HW8 - CSE21 FA11 Homework#8 8.1 An urn contains r red...

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CSE21 FA11 Homework #8 (11/14/11) 8.1. An urn contains r red marbles and b blue marbles. A random marble M 1 is drawn out. If M 1 is red, then it is put back into the urn along with c more blue marbles. On the other hand, if M 1 is blue, then it is put back into the urn along with d more red marbles. Now, a second marble M 2 is randomly drawn from the urn. (a) What is Pr ( M 2 = red )? (b) What is Pr ( M 2 = red | M 1 = red )? (c) What is Pr ( M 1 = blue | M 2 = blue )? 8.2. A biased coin C has Pr ( head ) = 2 3 , and Pr ( tail ) = 1 3 . The coin is ﬂipped n times, resulting in the sequence ( F 1 ,...,F n ). Let X denote the random variable deﬁned by X ( F 1 ,...,F n ) = the number of heads in the F i . What is the expected value E ( X ) and variance V ar ( X )? 8.3. The Acme Grommet Company manufactures grommets (whatever they are!). Unfortunately, their quality control processes aren’t very good, so it turns out that in any batch of grommets produced, the fraction α are de- fective (= bad), while the fraction 1

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HW8 - CSE21 FA11 Homework#8 8.1 An urn contains r red...

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