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practicum2

# practicum2 - ISYE 2028 A and B Spring 2009 Practicum 2 Dr...

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ISYE 2028 A and B Spring 2009 Practicum 2 Dr. Kobi Abayomi January 23, 2009 Please be able to show all of own your work and reasoning. Include computer printouts where you can. You won’t need Good Luck. Due Thursday March 5th - In class 1

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1 1. At one point the claim was made that California is deadlier than Iraq is to American servicemen. The murder rate in 2004 in California was 6 . 5 per every 100 K people. This worked out to 2,394 homicides in California in 2004. The latest total of American military casualties 1 is 2058 between 3 / 2003 and 10 / 2005. Assume there are a constant 130 K Ameri- can troops in Iraq. Investigate the veracity of this claim, on its face. As well, comment on assumptions or misinterpretations of data that may be misleading 2. The president wishes to increase troop levels to 180 K in 2006. Assuming the war becomes no deadlier for American soldiers estimate the probability that more than 700 servicemen die in 2006. 1 From http://icasualties.org/oif/ 2
2 Do I AND Do II (I) If X χ 2 (5) determine the constants c and d so that P ( c < X < d ) = . 95 and P ( X < c ) = . 025 (II) Let X have a gamma distribution with pdf f ( x ) = β - 1 xe - x/β The E ( X ) = 28. Find the parameter β and P ( X < 9 . 49) 3

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3 Do I and Do II (I) Take two Poisson distributed random variables: X Poi ( λ X ); Y Poi ( λ Y ) Now suppose two separate random variables for the waiting time between events for X and Y . These random variables will be Gamma ( α, β ) distributed with α =the number of events and β = λ - 1 : U Gamma ( α, 1 X ); V Gamma ( α, 1 Y ). Assuming X and Y are independent, what is the probability that the U is greater than V ? You don’t need to evaluate your answer. OR (II) Take two Normally distributed random variables: X N ( μ X , σ 2 X ); Y N ( μ Y , σ 2 Y ).
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