# ps1 - are of the same length). The 2n parts are arranged...

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Homework 1, Statistics 430, Spring 2008 This homework is due Thursday, January 31 st in class. 1. Ross, Problem 2.1 in the Problems Section, pg. 55 2. Ross, Problem 2.6 in the Problems Section, pg. 56 3. Ross, Problem 2.21 in the Problems Section, pg. 58 4. (a) Ross, Problem 2.23 in the Problems Section, pg. 58 (b) Three fair dice are rolled, one red, one green, and one blue. What is the probability that the upturned faces of the three dice are all different? 5. Ross, Problem 2.29 in the Problems Section, pg. 58. 6. Ross, Problem 2.37 in the Problems Section, pg. 59. 7. Show that nC0 –nC1 +….+/-nCn=0. for all n. Notes: 1. nCk is the number of combinations of k items out of n. 2. The terms alternate in sign. The last term is either + if n is even or – if n is odd. Hint: It can be done by induction, but that is complicated. Consider using an appropriate theorem. 8. Suppose that each of n sticks is broken into one long and one short part (no two longs
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Unformatted text preview: are of the same length). The 2n parts are arranged into n pairs at random from which new sticks are formed. a) Find the probability that the parts will be joined in the original order. b) Find the probability that that all long parts are paired with short parts. Hint: label the 2n pieces L 1 ,…,L n and S 1 ,…,S n . You may start with L 1 (without loss of generality) and see what its probability of being paired appropriately. Then take any part not assigned and see what its probability of being paired appropriately assuming that L 1 is paired appropriately, and so on. When cells are exposed to harmful radiation, some chromosomes break and play the role of our sticks. The “long” side is the one containing the so-called centromere. If two “long” or “two” short parts unite the cell dies....
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## This note was uploaded on 04/17/2008 for the course STAT 430 taught by Professor Krieger during the Spring '08 term at UPenn.

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