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Unformatted text preview: T exceeds 35. (Hint: use ( t ) 1 2 + t (4 . 4-t ) 10 , 0 t 2 . 2). (c) What is the probability that the temperature exceeds 35 on at least one day during the month of July? (Important hint: there are 31 days in July). 3. Let X be a continuous RV with PDF 20 marks f ( x ) = ( 2 | x | 3 ,-1 < x < 1 , otherwise Using the method of transformation, nd g ( y ), the PDF of RV Y = 1-X 2 . 4. Let X be a Laplacian RV with parameter > 0. The PDF of X is given by 20 marks f ( x ) = 2 e- | x | , x R (a) Find the characteristic function of X . (b) Using the result in part (a), nd E ( X ) and E ( X 2 ). 5. Let X and Y be jointly continuous with joint PDF 20 marks f ( x,y ) = ( 4 xy if 0 x 1 and 0 x 1 , otherwise . (a) Compute the probability that Y X . (b) Find the marginal PDF of X and sketch it. 1...
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- Summer '08