Prove: Let X₁, X₂,..., X„ be a r.s. from N(µ,σ²) and Y₁,Y,₂,..., Y be another independent r.s. from N(μ₂,₂²). Then, (X-Ỹ)-(μ₁ −μ₂) t(n₁+n₂-2) assuming o = 2, 1 1 m M₂ where S = (n − 1)S² + (n₂ −1)² m₂ +1₂-2 Some hints: (n₁ - 1)S (n2 - 1)S2 (a) Determine the (marginal) distributions of and 02 02 (b) Use the fact the chi-square distribution is reproductive to find the distribution of (n₁ - 1) S² 02 (n₂ - 1)S2 + 02 ·+·

Q: If u = x+ 1 t = vu y = t? then, = 0 dy dx dy 2. = x dx dy 3. = 1 dx dy dx 1. 4.

A: (3) We have to find out dydx

Q: = f(x,y, z) = x + sin y and Calculate if w ди x = x(u, v) = In (u + v), y = y(u, v) = e".º and z =…

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Q: 5. Suppose z = f (x, y), where x= g(s,t)and y= h(s,t). Show that ôz d²x ¸ ôz ô²y %3D ô°z ôx ôy ôz(…

A: Chain rule of partial derivatives: Let us consider a two variable function  z=f(x,y)  where ,…

Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

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Q: 1. Let f(x,y,z) = 2.x* +8yz' +8 . Find f(0,5,1). A) 48 B) 128 C) 48 D) 9 E) 22

A: Given f(x,y,z)=2x3+8yz3+8f(0,5,1)=2(0)3+8(5)(1)3+8

Q: 3. u, = u, - sin x cos t, 1 >0 В.С.: и(0, г) %3D0, = () 1.С.: «(х, 0) %3D 0, u,(x. 0) = 0

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Q: Let M = = Mu= + + 24 4x + 2y Mv = (4:+2w = = (x, y), v = (z, w). Find the followi X X 4x + 4y 4 + 4w…

A: Given that M=4424, u=x,y, v=z,w

Q: dz; |z – i| = 1 (z – i)3

A: We have to use the Cauchy integral formula to evaluate the following integral ∮ ez2z-ι3dz over the…

Q: 4. Let S and T be stopping times for a filtration (Fn). Let M N = max(S, T). (a) Show that M and N…

A: Since I have solved similar ones,let us solve the problem step by step by proving m and n are both…

Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: 1. R= {(1, 1), (2, 2), (3, 4), (5,9)} C ZX Z 2. R= {(n, m) ENXZ: n² = m} CNXZ 3. R = {(n, m)…

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Q: Let A = {x E Z: 8lx} and let B={EZ:12lx}. Then None of these ВС А O ACB O A=B

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Q: What is the antiderivative of J (5t° 2t* + t + 3) dt. c.t° -+t + 3t 2 а. t5 +t2 + 3 с. b. t° -t5 +t2…

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Q: YA (1,0) C is the path from (1, v2) to (1,0) along line segments as shown in the figure above. Then…

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Q: 100 X~Nμ. Σ) where μ= 50 10 0 then f(x 2,X2 : 0 5 and X1-100 -1/2[(- 10 (1/44.43)e 5 ylgn İhi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 4) Find ôw/ ôr if w= x=r-s, y= cos(r + s), z = sin(r + s) at the point (r,s)= (1,–1) Ans. 12

A: Find partial derivative using chain rule then put values of x ,y,z in obtained expression then put…

Q: Evaluate SSS10e=²+y²+z?)"* dV over B where B = {(x, y, 2) : æ² + y² + z² < 1}. Take T = 3. Türkçe: B…

A: Triple integral is used to integrate the function of three variable over three dimensional region.…

Q: Let f(x, y, z) = xy + e² and g(x, y, z) = y² sinz. Compute (a) D(fg)(0, 1, T). (b) D()(0, 1,5).

A: Given that fx,y,z=xy+ez and gx,y,z=y2sinz. We know that if f:ℝ3→ℝ is a function, then…

Q: 2t k, then the distance traveled over 0Sts In 3 is:

A:

Q: cu Ifu =(x* +2yz,y +2:x )Prove that (y' - a)+(x-y= + (-xy) cu =0. - EX

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Q: 2. Suppose that X and Y have the following joint PMF: P» (x,y) Y X 1 2 0.10 4 0.15 6 0.10 0 0.15…

A: The joint PMF of X and Y is  PX,Y(x,y)              Y X 0 1 2 2 0.15 0.10 0.10 4 0.20 0.15…

Q: 3 13. If x = u + v³ and y = uv – v² are solved for u and v in terms of x and y, evaluate ди ди dv dv…

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Q: Question 1 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error…

A: The independent variables are Real income and Real Wealth. The given output represents multiple…

Q: Find for the function h(x, y, z) h(x, y, z)= ecos(y +8z).

A: Given,           hx,y,z=e7xcosy+8x

Q: W.Find A' for the given cholce of U. 1A (3,6, 9) U (x/0<x$ 10 A 2. A = (1, 2, 3) U = (0, 1, 2, 3, 4,…

A: From the given information we find the A compliment .

Q: y let f(v₁v₁w) = (eº, cos(utv) tsin (utv+W)) and g(x, y) = (e², (os (y-x), ey). Calculate fog and…

A: