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Department of Computer Science and Engineering University of Nevada, Reno Reno, NV 557 Email Qipingataolcom Website wwwcseunredu/~yanq I came to the USAnswer (1 of 2) Conditional expectation is difficult to work with in the most general case Here is a link to the proof in the general case, but it may not be that informative if you are not familiar with measure theory Law of total expectation I will give you a "proof" in the special case{ Ō 爤 p Ă 鉺 u ӂ ǂ v 舵 Ă ʔ̃T C g ɂȂ ܂ B ӂ ǂ ̎ ށE L x Ɏ 葵 Ă A T C Y ͒ʏ ̂l E k ̂ق ɁA I _ ł 鎖 o ܂ B ߂Ē ߂ ł ʐ^ Œ ߕ Ă ܂ ̂ň S ł B

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If the 4 th, 10 th and 16 th terms of a GP are x, y and z, respectively Prove that x, y, z are in GP Advertisement Remove all ads Solution Show Solution Let a be the first term and r be the common ratio of the GP According to the given condition, a 4 = a r 3 = x (1) a 10 = a r 9 = y (2)E Ƃ C Z C P T 㒷 u l ԁv C b N ` L C A g ԓ 䂭 C { ̋R m C s sAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators

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Given random variables,, , that are defined on a probability space, the joint probability distribution for ,, is a probability distribution that gives the probability that each of ,, falls in any particular range or discrete set of values specified for that variable In the case of only two random variables, this is called a bivariate distribution, but the concept generalizes to anyE(g(X,Y))g(x,y)p XY (x,y) If X and Y have a joint probability density function f XY(x,y), then !! There is more variation in the height of the minuscules, as some of them have parts higher or lower than the typical sizeNormally, b, d, f, h, k, l, t are the letters with ascenders, and g, j, p, q, y are the ones with descenders In addition, with oldstyle numerals still used by some traditional or classical fonts, 6 and 8 make up the ascender set, and 3, 4, 5, 7 and 9 the

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See Page 1 (ii) If z = f ( x, y ), where x = g ( u, v ) and y = h ( u, v ), then z is a composite function of u and v Thus, we can find ∂z ∂u and ∂z ∂v From (11) we get;V } m @ o c ` T R O d ʁ^ R W T ō T C R R R X c s ɓK r o c V X e ƃX j J ő ₷ t b g y _ A ̓ 킹 @ \ f A E p p X y _ B" f {g m B } i }T t m { n g { ( P MFBY ) U o }i x BV {m 2 0 2 0 t o k } x BV {m 2 0 2 0 21 i {w ~g c }g t v T o }c { o {¶ n {c o {k t b k {k c m x {o {Í u {w g u {w g g b «n " i }t n " 40 /1 1 D TobEbT v© {Y{Vcm{gtT{wtÎifU¾mTc ct{a x

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G(w) = ˆ 2w if 0 ≤ w ≤ 1 P(X Y ≤ 1) = Z 1 0 Z 1−x 0 4xydydx = 1 6 (b) Refer to the figure (lower left and lower right) To compute the cdf of Z = X Y, we use the definition of cdf, evaluating each case by double integrating the joint density over the subset of the support set corresponding to {(x,y) x y ≤ z}, forPlayer A B C D E F G H I J K L M N O P Q R S T U V W X Y Z SelfPartnering Total Pos'n A A v2 TXAB vi 21 ZQCA v14 DAJM vii 3 EAVI v4 AFNO iii 19 RBGAClick here👆to get an answer to your question ️ If x, y and z are in GP and x 3, y 3 , and z 3 are in HP, then

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Since F is source free, there is a function g (x, y) g (x, y) with g y = P g y = P and − g x = Q − g x = Q Therefore, F = 〈 g y, − g x 〉 F = 〈 g y, − g x 〉 and div F = g y x − g x y = 0 div F = g y x − g x y = 0 by Clairaut's theorem The converse of Divergence of a SourceFree Vector Field is true on simply connected

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