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Unformatted text preview: (25) 2. In a skiing competition, a competitor's overall time is found by adding his time X in the downhill section to his time Y in the slalom section. Downhill times have an expected value of 75 seconds with a standard deviation of 5 seconds. Slalom times have an expected value of 105 seconds with a standard deviation of 6 seconds. Overall times have a standard deviation of 11 seconds. Assuming quadratic loss, what is the optimal linear prediction of the expected overall time of a competitor who has recorded 70 seconds in the downhill section? 3. Let X and Y have p.d.f. (10) (a) Find c. (15) (b) Find Prob (X $ Y). (25) 4. Consider Example 2.4.2 on pp. 48-50 of the text. Consider the random variable Z = E(Y 1 * Y 2 ). Find its density function....
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- Fall '10