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Unformatted text preview: Statistics 5101, Fall 2010: Homework Assignment 8 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 81. Let X have the standard Cauchy distribution, which has PDF defined in the brand name distributions handout f ( x ) = 1 π · 1 1 + x 2 ,∞ < x < ∞ . (a) Find the quantile function for X . (b) Find the median of X . (c) Find the lower and upper quartiles of X . Hint: the indefinite integral of 1 / (1 + x 2 ) is arc tangent of x (inverse of the tangent function). 82. Suppose X has the Exp(1) distribution. (a) What is the best prediction of the value of X if minimizing expected squared error is the criterion? (b) What is the best prediction of the value of X if minimizing expected absolute error is the criterion? In this problem, we want numeric answers so we can see how different they are....
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This note was uploaded on 12/01/2010 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.
 Fall '02
 Staff
 Statistics

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