{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Statistics Homework Solutions 39

# Statistics Homework Solutions 39 - 39 SECTION 2.6 10 05 10...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 39 SECTION 2.6 10 05 10 05 5x2 Â¡ 9 95 Â¡ 10x dx 10 Â¡ (d) ÂµX 9 95 51 51 2 5y2 Â¡ Â¡ 49 Â¨ 5y dy 5 Â¡ (e) ÂµY 49 50 Â¡Â¥Â¤ Â¡ Â¡ Â¡ Â¡ Â¡ Â¡ Â¤ Â¡ e1 e 0 2325 1 e 1 2 Â¡ Â¡ Â¨ âˆž x 0 Â¡ Â¡ Â¡ Â¡ Â¡ Â¡ (d) Since X and Y have the same probability mass function, ÂµY ÂµY âˆž f x y dy dx âˆž 2x e xy dy dx Â¡ Â¥ 0 2x Â¡ 2 y e Â¡ x Â¡ e Â¡ 0 0 Â¤ x 1 Â¡ e ex 2 2 Â¥ Â¥Â¤ âˆž 2 0 0 2. 2x Â¢ Â¡ 2 Â¡ Â¨ Y 1 Â¢ Â¢ (e) P X 1 Â¡ ÂµX Â¢ Y Â¡ Therefore ÂµX dx dx Â¡ e 0 ÂµX 1 Â¡ Â¤ 0 0 0 Â¡ dx x Â¥ e Â¡ âˆž Â¢ x xe Â¡ Â¡ 0 Â¡ dx 1 Â¤ Â¦Â¥ Â¤ Â¨ e Â¡ x e y Â¥ Â¥ xe x 0 1 dy âˆž e y Â¡ Â¡Â¥ Â¤ 1 âˆž âˆž e 1 Â¡ Â¤ Â¨ 0 âˆž Â¡ Â¥ Â¤ (c) ÂµX Â¡ dx x e 1 Â¥ Â¡ 1PY 1 Â¡ PX 0 Â¡Â¥ Â¤ 1 Â¥Â¤ 1 and Y x 0 and y otherwise 0 Â¥Â¤ (b) P X xy e 1. 1 y Â¡ Therefore f x y e if y Â¡ Â¡ 23. (a) The probability mass function of Y is the same as that of X , so fY y Since X and Y are independent, f x y f X x fY y . 0 and fY y Â¡Â¥Â¤ 10 5 0 if y Â¨ Â¡ ÂµX ÂµY Â¤ ÂµXY Â¡ Â¥ Â¤Â¥ (f) ÂµA 0. Â¤ ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online