W = U. W = 5, and ||W||2 a, then the value of a is: If U =

Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

Q: a. If p=√q=ra and pqr = 1, show that, x + y + z = 0.

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Q: Given y, = Bo + Bıyt-1+ E; and ɛ, i.i.d. N(0, o²), compute: (a) E(y;). (Ъ) Var(y;).

A: Given information: In the given model the current period is predicted on the basis of its preceding…

Q: Given: z = x² + xy³, x = uv² +w³, y=u+vew əz Find when u = 1, v = -1, w=0 Əv

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Q: Let X, X2,...,Xg i.i.d B(1,p), where p = p(x,= 1) E (0,1) the UMP test for Ho: P=0.5 VS H: P > 0.5…

A: A): option (a) correct c=6, y=0.138 B): exponential form of distribution is not true (False)

Q: The sutiable substitution for evaluting csc' (x)cot°(x)dx is CS a) u = tamx (b)u = cotx (c) u= cscx…

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Q: In PCA, we obtain z E Rk from x E R" as follows: T z = u(1) y(2) u(k) Which of the following is a…

A: Given that,In PCA, we obtain z∈Rk from x∈Rn as follows:z=|u(1)| |u(2)| ...…

Q: Given o = y x² + 2y – z and ū = î – 3ĵ + 2k , i ƒ Vþ at the point (1, 1, 1) is perpendicular to ū,…

A: Given two vectors, ϕ=γx2+2y-z and u→=i -3 j +2 k. To determine ∇ϕ. ∇ϕ=2γx i+2 j-k Now at the point…

Q: Let C: |z-il=3 and I = $. , dz. Then e 3z z2 |= 6ti |=0 |= 8Ti |= 4Tti None of these

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Q: 4. Let v = (2,1), and c = (3,2) such that v.r= 4, and cx = 1. then x = c) (9,14) %3D (5.3) D7-10) d)…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: If v = a,i + bịj and w = a,i + bąj, then v + w = ( )i + (_)j v - w = ( )i + (_ kv = ( i + (_)j. _)i…

A: Given v→=a1i→+b1j→w→=a2i→+b2j→ v→+w→=a1i→+b1j→+a2i→+b2j→…

Q: p + q N = p = u + vw, q = v + uw, r = w + uV p + r aN an aN when u = 4, v = 3, w = 5 au' av' aw ƏN 1…

A: We have to find the derivative by chain rule As per guidelines we have to solve one question

Q: Let C: z-i-3 and I = 4, dz. Then %3D |=0 |= 6rti |= 8ti O I= 4rti None of these

A: third option is correct

Q: If r(t) = (e³t, e-4t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = II T(0) = r"(0) =…

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Q: x3+y3 x+y If u = = In ди X ?x In ( ди + у ду then find the value of ?

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Q: The sutiable substitution for evaluting csc' (x)cot (x)dx is (a) u = tamx (b)u = cot x (c) u = cscx…

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Q: (a) Let U~ uniform[0, 2], and let U S= Se Find (i) E[S], (ii) P(S≥ 0.5). (b) Repeat (a) if U~ exp(2)…

A: Given: S= ∫0Ue-sds

Q: x then ux is XX If u = V y %3D

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Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

Q: Find the uncertainty in U, assuming that X = 10.0 ± 0.5, Y = 5.0 ± 0.1, and a) U = XY² b) U = X² +…

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Q: If X=t X ,then W(x,(t), x(t)) = 1 0 Select one: a. Cet

A: Given that : X'=1tt10 The determinant is : X'=1t0-t.1=-t The Wronskian is given by ,…

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: Given: z = a4 + ry°, a = uv* + w*, y = u + ve" Find when u = 1, v = 3, w = 0 dw 48r3 + 12y2 + 2xy X…

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Q: S = {(x, Y, z) E R³ : 2? = x² + y², 0 < z < 4}. Evaluate e*dS.

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Q: 13. Given u = and v = , find: a) u + v b) 2u - v c) Ju|

A: Given that u= &lt;-3, 5&gt; and v=&lt;4, -7&gt;   a) u+v = &lt;-3, 5&gt; + &lt;4, -7&gt; = &lt;-3+4,…

Q: If u = cot ди then x x- y

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf (2,-1, 1) = =, then %3D A) B) 11 C) D) E)

A: The function is given by fx, y, z = ln2+x2-2y2-3z The vector is given by u→ = 1, 1, -1 To evaluate:…

Q: If u -x2 + y? + z² be such thatr u,+ yu, + zu̟ = Àu, then A is equal to %3D + A.1 В.2 C.0 D. none of…

A: Given that, u=x2+y2+z2 Then xux+yuy+zuz=λu The aim is to find the λ value, ux=2xuy=2yuz=2z

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (c) z = x2 + 2y2 ; x = es - et, y = es + et

A: Formula to find the partial derivatives helps to find the partial derivatives of the function with…

Q: Find a and b such that v = au + bw, where u = v = (7,2) a = b || || = (1, 2) and w = (1, -1).

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Q: af af af Find and 1, ax' əy' az f(x, у, z) %3D 17хyz

A: Given,           fx,y,z=17xyz

Q: S(r, y) = S2, 0<r<y< 1, 10, elsewhere. Determine if X and Y are independent.

A: We have to check whether , X and Y are independent First we will find out the marginal probability…

Q: If X and Y are independent RVs following N(8, 2) and N(12, 4/3 ) respectively, find the value of 2…

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Q: Given: z = = x* + zy°, * = ww* + w, y = u +ve" a z Find when u = - 3, v = 2, w =

A: Given: z=x4+xy3x=uv4+w4y=u+vew The objective is to find ∂z∂u, when u=-3, v=2, w=0

Q: You are given P(A U B) = 0.8 and %3D .P (A U Bº) = 0.9 %3D Calculate P(A) 0.7 0.2 0.1 0.3

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Q: Show that if X and Y are independent rv's, then E(XY) = E(X) · E(Y)

A: we have given that, x and y are independent random variables, then, we will prove, E(XY)= E(X).E(Y),

Q: A GIVEN: AB I BD, ED I BD. PROVE: XA = XE. C

A: We will use these three concept here  1- perpendicular makes an angle of 90° 2- vertical angle are…

Q: 2. Given V = x + y' av a) Find and b) Hence, show that y ( - ) = v. = V. ду

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). v = (0, 24) V = a = b =

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Q: Sw (a) Given w(x, y, z) = 2xyz,x = s² + t², y =, and z = In t, find and 8s Sw St

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: e EC QP] × U di © T

A: Visitors from Jan Feb Mar Apr May Jun Tot SA 15 8 C D 9 5 66 Abroad A 3 13 26 4 6 62 Total 25…

Q: (b) Evaluate at the point (s, t) = (1, 2). Əsət

A: As per requirement, we we solve part b) only Given function is z=fst-3,s2+t3 f1-1,9=3, f2-1,9=7,…

Q: Let z = a?y – ry?, x = e 4, y = e2t, then which of the following is 2e2t + 2e 2t a. O b. -2e2t – 2e…

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Q: The soluhion of P.D.E 3 + 2 du o, u(x,0) = 4e* is @ 4e © 4e O 4e

A: 3∂u∂x+2∂u∂y=0, ux, 0=4e-x Characteristic curves are given by  dx3=dy2=du0 Solving the first two,…

Q: If C is given by x = 2t, y = −2t, z = t, 0 ≤ t ≤ 2, evaluate Z C (x − y + z) ds

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Q: If X and Y are independent, then p(X, Y) = 0

A: The basic rules for mean and variance when two variables are independent are  E[XY] = E[X] E[Y]…

Q: a) Is it reasonable to assume X; and Y; are independent? b) Is it reasonable to assume X; is…

A: According to the answering guidelines,  we can answer only three subparts of a question and the rest…

Q: Let C: |z – i| = 3 and I = $. dz. Then e 6z z2

A: By using Cauchy integral's formula for nth derivative.

Q: Given f(u, v), where u = x² y, v = xy? If at the point (2,3), f, = 4, fm = 3, fm = 5, ƒ, = 1, fm =6.…

A: Given; u=x2y, v=xy2

Q: Let a A =| d e f h i and 2a 2b 2с B = 2d 2e 2f i Given that det(A)=1/12, what is det( B-)? Answer:

A: Other