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MAE 371, Chapter 17, Page 12 () 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 0 2 sin45 sin45 012 J 2 1 1 1 2 sin90 sin90 012 J 4 12 2 2 J o o o o T V E l E mg Mg l T V E l E ml ml Ml mg Mg l E E E. H i Y F ̏ ہE L X v D ꂽ E C X J r L SARS MARS V ^ R i E C X ȂǂɎg p Ă 鎟 f _ i g E Z x Ō ʂ𔭊 P A E t H NO3 ʐM ̔ e N m e N m Ђł͈ ʉƒ ` H X ` H i H Ȃǂ̊Q 쏜 i S L u A m ~ A _ j A n G A A i L V A } _ j A V ~ A V A A A A q A A L N C V A V o V A ` ^ e V A X Y o ` A A V i K o ` A ~ c o ` A q A i N W A J V A N Ȃǂ̋쏜 ͑΍ j A Q b 쏜 i l Y ~ A C ^ ` A A C O } A n N r V A. J for each j Since each X j is closed, we have x j 2X j for each j Hence (x 1;;x n) 2X 1 X n 3 Let (M;d) be a metric space Let >0 and let y2M Prove that the closed ball fx d(x;y) g is a closed subset of M Solution Let z be a limit point of fx d(x;y) g So there is a sequence fz ngsuch that z n2fx d(x;y) gfor all nand lim n!1z.

M O ͒n 𒆐S ɁAWeb i z y W j C X g ̐ 쓙 T g ܂ B c f U C \ 󂠂 ܂ A ł B. NaLASystemH )Y z ½ È p · Â0 ÒGEGGGTGnH FûFôFÔFö 6õ4 ¤ %Ê'2 ¾Walton and Polachek, 1960 êç $ GwG2G ,´5 H R > 9 H lampedmass model ¾Thresher, R, and Nath, J 1975 GdG2 $ (Ô e8 2 lampedmass model NaLASystemH )Y z ½ È p · Â0 ÒGEGGGTGnH FûFôFÔFö 2. Y @ I b N X V c(S @ u g p Y) N t H ɂ A D ꂽ h V m A C s C g I b N X t H h V c B J Ԃ Ă ʂ͎ A ^ h ł ܂ B הԎ g p s C g I b N X t H h Ȃ ł͂̂ Ȃ₩ Ȏ ƗD Ȍ 򊴂 ͂ł B ʋC A z ɗD ꂽ 100 ComfortCloth iR j ō ꂽ ̃I b N X t H h V c ́A ł Ƃ G ŁA r W l X J W A ܂Œ Ȃ ̕ L ܂ B P b g ɁA ܂̓{ ^ _ E A w ʂ̓Z ^ v c ̎d l ł B.

F B J C X g V T C g I w ̃X g b N C X g C u ł I @ V ނɂ J e S ł B ݃f ^ 𐮔 ɂ ɂȂ Ȃ ܂ B. Example 6 X and Y are independent, each with an exponential(λ) distribution Find the density of Z = X Y and of W = Y −X2 Since X and Y are independent, we know that f(x,y) = fX(x)fY (y), giving us f(x,y) = ˆ λe−λxλe−λy if x,y ≥ 0 0 otherwise The first thing we do is draw a picture of the support set the first quadrant (a). T P B Y J P Q O Y W V P J Q Y W M S Y A P J B Y M V I X L M B D Q 2 4 L R N M A Q Q D F Z R T L Y N Y A E O R L Y P 4 T E 4 S Y 4 P T R S Y S N R Y A E N R 7 4 my whole family figured it out but i can't?.

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