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Assignment 8 Solutions

Assignment 8 Solutions - CE93-Engineering Data Analysis...

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Unformatted text preview: CE93-Engineering Data Analysis Joan Walker, Spring 2011 Assignment 8 Due 4/6/2011 11:10 AM 1. A drunk staggers out of a bar and attempts to walk down the street toward his home, which is located on the same street 1000 feet away. Since he is staggering, the distance covered in a step is random. In particular, the distance covered in 1 step has the following probability mass function: ¡¢£ ¤ ¥¦§¨ ¡©£ ¤ ¥¦¢§ª ¡«©£ ¤ ¥¦¢§ (A negative value means that the step took him further from, instead of toward, his house—he is really drunk!). Each step taken is independent of other steps. a. (7 points) What is the expected value of the distance covered in one step? Let X be the distance covered by one step. E(X)=0.5*2+0.25*1+0.25*(-1)=1 b. (7 points) What is the variance of the distance covered in one step? E(X 2 )=0.5*2 2 +0.25*1 2 +0.25*(-1) 2 =2.5 Var(X)=2.5-1 2 =1.5 c. (7 points) What is the (approximate) probability that he has not reached his home after taking 900 steps? Let Z=X 1 +X 2 +…+X 900 According to central limit theorem, the distribution of Z can be approximated by a normal distribution with mean of 900E(X) and variance of 900Var(X). ¬¡­ ® ©¥¥¥£ ¤ ¯¡ ­ « °¥¥±¡²£ ³¥´µ¶·¡²£ ® ©¥¥¥ « °¥¥±¡²£ ³¥´µ¶·¡²£ £ ¤ ¸¡ ©¥ ³¹©¦§ £ ¤ ¥¦°°º» 2. Summer thunderstorms in Cleveland air traffic control center airspace occur at a rate of 0.5 per day over the 16 week period from May to early September. Thunderstorms are considered to be independent events. a. (7 points) What is the probability that on a given day there will be at least one thunderstorm in this airspace?...
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Assignment 8 Solutions - CE93-Engineering Data Analysis...

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