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Unformatted text preview: Btu and standard deviation 25 million Btu. ( a ) What can you say about the proportion of the population that used between 103 and 203 million Btu during that year? ( b ) Estimate the proportion of the population that used in excess of 228 million Btu during that year using two diﬀerent estimates learned in class. Which one gives a better bound? Problem 5 Let X be a Pareto random variable, with the density f X ( x ) = 4 x5 , x ≥ 1 , and equal to zero otherwise. 1 ( a ) Calculate both the exact probability P ( X > 3) and the upper bound given by the Markov inequality. Is the upper bound very tight? ( b ) Calculate both the exact probability P (1 ≤ X ≤ 5 / 3) and the upper bound given by the Chebyshev inequality. Is the upper bound very tight? Due:October 18, at 4 p.m. 2...
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 '08
 WEBER
 Standard Deviation, Variance, Probability theory, probability density function, moment generating function

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