Prove that x^-1/x^-1 y^-1 x^-1/x^-1-y^-1=2y^2/y^2-x^2 174454

 Question 28 (OR 1st Question) If √(1−𝑥^2 ) √(1−𝑦^2 ) = a (x − y), then prove that 𝑑𝑦/(𝑑𝑥 ) = √(1 − 𝑦^2 )/√(1 − 𝑥^2 ) Finding 𝒅𝒚/𝒅𝒙 would be complicated here To make life easy, we substitute x = sin A y = sin B (As √(1−𝑥^2 )= √(1−sin^2⁡𝐴 )=√(cos^2⁡𝐴 )) And then solve Let's substitute x

Prove that x^-1/x^-1 y^-1 x^-1/x^-1-y^-1=2y^2/y^2-x^2- 1 First make the equation into x^22x1 >= 0 by rearranging and multiplying by x You should find it is (x1)^2 so for any x (not just x>0) this function is greater than or equal to 0 because of ^2 For your situation it is obvious that x>0 which is certainly true for the factorised function Therefore you have proved that x1/x is greaterExample 1 X and Y are jointly continuous with joint pdf f(x,y) = ˆ cx2 xy 3 if 0 ≤ x ≤ 1, 0 ≤ y ≤ 2 0, otherwise (a) Find c (b) Find P(X Y ≥ 1) (c) Find marginal pdf's of X and of Y (d) Are X and Y independent (justify!) (e) Find E(eX cosY) (f) Find cov(X,Y) We start (as always!) by drawing the support set (See below, left) 2 1 2 1 1 x y=1−x y x y support set

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Stack Exchange network consists of 178 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 Exchange texx ^ 2 xy y ^ 2 = \left x ^ 2 2 x \left( \frac{1}{2} y \right) \left( \frac{1}{2}y \right) ^ 2 \right \frac{3}{4} y ^ 2/tex I'm almost spilling out the answer Since the OP has already had his own solution, this is just another way to tackle the problem So, what left is to determine when the equation holds ) #9 njama 216 1 There is much easier way to

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