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May 08, 18 · F(x, y, z) = yz i xz j (xy 18z) k c is the line segment from (1, 0, −1) to (5, 6, 1) (a) find a function f such that f = ∇f f(x, y, z) = (b) use part (a) to evaluate c ∇f · dr along the given curve cZ Q b q U z I ñ u c I ² C r M h P v U \ y,)5 z D S ¢ ñ Ó é ¦ ñ ´ s U ¤ ¥ s, r X } ` v ¸ ê × é r a K b q ô W ® ß ` j ¸ 3&5 G S < ¤ ¥ V / b j ° d r ¤FDVH IDWDOLW\ UDWH &)5 ¥ z ¤ ¥ s d ç H ^ y1(x) = Z 1 x 8xydy = 4xy21 x = 4x(1−x2),0 < x < 1 (c) Find the marginal probability density of Y, f 2(y) Answer f 2(y) = Z y 0 8xydy = 4yx2y 0 = 4y 3,0 < y < 1 (d) Are X and Y independent?

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May 01, 19 · Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeMay 07, 21 · ­µÎ®¦´ ª´Á¨ ­µÎ ´ µ µ¦Á · ¤¸ ´ ¸ Ê ¦·¤µ µ¦ ¨· ^ ¨oµ ´ y y

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