Statistics Homework Solutions 44

# Statistics Homework Solutions 44 - 44 CHAPTER 2 Â 0 1 e 6 0...

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Unformatted text preview: 44 CHAPTER 2 Â¡ 0 1 e 6 0 x2 y3 3 2 Â¥ 3 Â¦ Â¨ 2 and Y dy dx Â¦ 11. (a) P X 3 Â¤ Â¨ y3 dx Â¦ 0 1 1 e x2 dx Â¥ Â¡ 1 e 2 Â¤Â¦ Â¡ Â¡ 0 Â¡ 2 e 0 x2 Â¦ 1 e 2 Â¡ 2 2 1 Â¤ Â¡ Â¤ 1 Â¡ 0 3996 Â¡ 0 12 Â¥ Â¡ Â¡ Â¨ 3 x2 y3 Â¡ 3 1 e 6 Â¦ âˆž âˆž dy dx Â¦ âˆž Â¦ Â¡ Â¡ Â¡ 3 Â¦ Â¡ Â¨ âˆž e x2 Â¡ Â¦ Â¡ 0 y3 Â¦ Â¡Â¥Â¤ Â¦ Â¨ Â¡ y 0 1 e 3 Â¡ Â¨ Â¦ Â¦ 0 dx y . y3 . 0. 0 Â¡ y3 x2 0 1 e 3 Â¦ 1 e 3 0 1 e 2 Â¦ x2 y3 y3 0 Â¡ Â¦ 1 e 6 e Â¦ x Â¡ 0 x âˆž x2 Â¦ x2 1 e 2 Â¡ dy x2 y3 Â¦ Â¡Â¥Â¤ 1 e 6 0. Â¡ Â¡Â¥ Â¤  Â¨ Â¡ Â¡Â¥Â¤ Â¡Â¥Â¤ Â¡Â¥ Â¤  Â¨ Â¡Â¥Â¤ Â¡ Therefore fY y 3 dx x2 0 for all x so fY y âˆž Â¡ 0, fY y Â¦ If y 0 f xy 1 e 52 0 0821 1 e 2 Therefore fX x (d) If y Â¦ 0 Â¡ âˆž e âˆž 0 for all y so f X x 0, fX x If x x2 Â¡ Â¤ 0 f xy e 1e dx 3 Â¡ Â§ (c) If x 1 e 2 3 y3 e Â¦ âˆž x2 Â¡ 3 1 e 2 Â§ âˆž Â¦ Â¥ 3 Â¥ 3 and Y e (b) P X 1e Â¦ e x2 Â¡Â¥Â¤ ...
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