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SOLUTIONS TO SECTION 1 5 Solution We have u x=u ss x u tt x= u s 2u t u xx=u sss x u stt x 2u sts x 2u ttt x= u ss 4u st 4u tt u xy=u sss y u stt y 2u sts y 2u ttt y= u ss 2u st u y=u ss y u tt y= u s u yy=u sss y u stt y= u ss Substituting10/3/18 1 (a) The case r= 1 of Chebychev's Inequality is known as Markov's Inequality and is usually written P(jXj ) E(jXj)= for an arbitraryClearly f(x;y) is nonnegative as it is zero outside of the range indicated above, and positive inside In order to check the second condition we need to integrate the pdf over the shaded region that is, the region where y Comunicacion 5 J a funk funeral home

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