hmwk4 - S TAT 6201 H OMEWORK 4 D UE O CT 4 2012 Read...

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S TAT 6201 H OMEWORK 4 D UE O CT . 4, 2012 September 28, 2012 Read Sections 2.1, 2.2 . For practice but not to be handed in: problems 2.6, 2.7, 2.10, 2.11, 2.14, 2.15, 2.17, 2.20 from the textbook. Hand in the following problems: 1. Let X have the uniform distribution on ( - π/ 2 , π/ 2) . Find the pdf of Y = tan X . This is the pdf of a Cauchy distribution. 2. Let f ( x ) = 1 / 3 , - 1 < x < 2 , zero elsewhere, be the pdf of X . Find the cdf and the pdf of Y = X 2 . 3. Suppose X has the Beta ( α 1 , α 2 ) distribution with pdf f X ( x ) = ( Γ( α 1 + α 2 ) Γ( α 1 )Γ( α 2 ) x α 1 - 1 (1 - x ) α 2 - 1 0 < x < 1 0 otherwise Find E( X ) . No gamma functions should appear in the formula! 4. Suppose U has the Unif(0, 1) distribution. What is the pdf of Y = - 1 λ log( U ) ? Suppose
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