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Unformatted text preview: (a) For what real numbers does there exist a constant c ( ) such that the function f ( x ) = c ( ) x , x > 1 is a PDF? (b) Suppose is such that f is a PDF. If X is a random variable having this PDF, for what positive real numbers does E ( X ) exist? 3 4. [10 pts.] Calculate the PDF corresponding to the DF F ( x ) = , x ( x + x 2 ) / 2 , < x < 1 1 , x 1 5. [10 pts.] Calculate the DF corresponding to the PDF f ( x ) = cos( x ) 2 , 2 < x < 2 Dene the DF on the whole real line. 4 6. [20 pts.] Suppose the random variable X has the PDF (not the DF) given by f ( x ) = 2 x, < x < 1 . Find the median (not the mean) of the distribution of X . 5...
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This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Spring '02 term at Minnesota.
 Spring '02
 Staff

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