Unformatted text preview: T exceeds 35. (Hint: use Φ( 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, ﬁnd g ( y ), the PDF of RV Y = 1-X 2 . 4. Let X be a Laplacian RV with parameter α > 0. The PDF of X is given by 20 marks f ( x ) = α 2 e-α | x | , x ∈ R (a) Find the characteristic function of X . (b) Using the result in part (a), ﬁnd 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
- Probability theory, Cauchy distribution, Prof. B. Champagne, Laplacian RV, faculty standard calculator