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Unformatted text preview: (b) ?±² , µ³?µ = 12 ² 2 7 + 6 ² 7 2 (c) ?±² , µ³?µ?² = 6 ² 3 7 + 3 ² 3 14 1 ² 1 ?² = 15 56 Problem 4.13 (PDF’s) (i) 2 1 ² ?µ = 2 , 0 < ² < 1 (ii) 2 ?² µ = 2 µ , 0 < µ < 1 (iii) No, since the product of the individual densities is not equal to the joint density. Problem 4.19 (Conditional PDF’s) (a) ? ¶ ±µ³ = ? · , ¶ ±² , µ³?² = 2 µ + 3 µ 14 1 , 0 < µ < 2. Hence, ? ?  ? ±²³´ = 12 ± 2 + 6 ±³ 4 + 3 ³ , 0 < ± < 1. Problem 4.32 (Expected Value) (a) E(4 + 16X + 16X 2 ) = 164 (b) E(X 2 + X 2 + 2X + 1) = 21 Problem 4.45 (Marginal PDF’s, Expected Value, Variance and Covariance) µ ± 1 ¶´ = · ¸ ¸ ¸ ¹ ¸ ¸ ¸ º 3 16 ¶ = 0 1 8 ¶ = 1 5 16 ¶ = 2 3 8 ¶ = 3 0 »¼ℎ½¾¿¶À½ Á µ ± 2 ¶´ = · ¸ ¹ ¸ º 1 2 ¶ = 1 1 2 ¶ = 2 0 »¼ℎ½¾¿¶À½ Á Â ? 1 ´ = 30 16 °Ã¾ ? 1 ´ = 19 4 − Ä 15 8 Å 2 = 1.234 Â ? 2 ´ = 3 2 °Ã¾ ? 2 ´ = 0.25...
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This note was uploaded on 06/02/2011 for the course CIV ENG 93 taught by Professor Staff during the Spring '08 term at Berkeley.
 Spring '08
 Staff

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