S479 S12 Quiz 2 Solutions

S479 S12 Quiz 2 Solutions - STAT 479 Quiz 2 Spring 2012 l A...

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Unformatted text preview: STAT 479 Quiz 2 Spring 2012 January 26, 2012 l. A two point mixture distribution of X is comprised of the following two distributions: X a. A uniform distribution where random variable is uniformly distributed between 100 and l 500 X L b. An empirical distribution with a mean of 100 and a standard deviation of 200. The weight for the uniform distribution is 0.6 and the weight for the empirical distribution is 0.4. Calculate the variance of X. L Dag/00S I Do 50473 “-1 Sb: “£63537” (gaw 3"“ 00:. “"’ 3‘90 I 3 3 9 199 ”’00)“ 00°) EKXT> : 3 XL(J/O‘>0§%$ Q3730.“ :: [5.3 fifig 33 0M =0Ilp 2:; E (x273 W t: we val; MEWS} (was «a I05?) see 4,2, as M . [EM (8?) ““ 0&0 FENDEIW all 5&5 e<atlg>fgg%am(®hlylm>e gang; p: (xi) {3, lg WM} shallg5K:>:{Q-f€l{l0%333.§> Wham; a maize VGA (X); Wfl wFfrfW 99 M» {321% aa tam; WWVW “WWW 2. You are given the following empirical distribution: 1 2 3 4 5 6 7 8 9 10 19 is the value of k in the standard deviation principle so that the risk measure under the standard deviation principle is equal to VaRQ75 (X) . k2 is the value of k in the standard deviation principle so that the risk measure under the standard deviation principle is equal to TVaRl75 (X) . Calculate k2 — k1. Lt “Ca «V? tgtgi‘im .. _,,,, M E<x>$ W+J . RM / 5,13 1 ”‘i/bqia‘angatl: ”all + gfie‘iew?” '2 , an M. 5o): WM“, . a mm » gas ...
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