Suppose X = (X1, X2, . .. , Xk) ~ Multinomial(n, p) , with p = (p1, P2, ..., Pk), prove that Cov(X;, X;) = -np;p; Hint: V(X +Y) = V(X)+V(Y)+ 2Cov(X,Y)

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

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Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: xo X1 Given the data set X2 X3 and the polynomials ỹo (x),ỹ₁(x), ₂(x) Yo Yı Y2 Y3 comprising the…

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Q: 1 (g) √ F+x(a+b)+abdx

A: To evaluate the following integral.

Q: Let M(x) = V3x – 6 and N(x) 2 Find the following: 2 - c) (N o M)(5) d) (No M)(홍) e) (No M)()

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Q: Use proof by contradiction approach to prove that VxM) V N(X)

A: This is a problem of Predicate Logic.

Q: Suppose that 7 '(t) = and 7 (0) = . Find 7(t) 7(t) = <

A: Suppose that r→'t=12t,e0.2t,t and r→0=1,-1,4. Then we have to find r→t=?

Q: Consider the interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

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Q: Let n:Z→ 2 the n(Z) =: %3D {3Z,1+3Z,2+3Z} {3Z,1+3Z} {3Z}

A: Let π:Z→Z3Z To find  : πZ

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: Let f(x) = 2x + x2 on [0,7]. Let p ={0,3,4,7}. Let a(x) = 2x2 on [0,7]. Give the numerical value of…

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Q: Given that P(X)= P(Y)= and P(XUY)= find 20 20 10 a) P(XnY) b) P(XIY)

A: Given,PX=920PY=720and PX∪Y=710

Q: Use the function to find the image of v and the preimage of w. T(V₁, V₂) =(√² V₁. √2, - V2, V1 + V₂,…

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Q: Let X~N(10,9). Find P(Z > -2)

A: It is given that, X~N(10,9)

Q: X 1 2 3 4 f(x) 2,6 3,5 3,2 2,4

A: From the given table, The general formula is,

Q: Let B = {1-3t +t² , 2 - 5t + 3t2, 1 + 5t2} and p (t) = 2 – 5t + 4t. Find x [p]g. %3D X1 = X2 = X3 =…

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Q: Either prove the wff is valid or give an interpretation that is false: (p.71) 18. (EEx)[R(x) V…

A: Introduction: The rules of inference are also applied in case of quantified propositions. Along with…

Q: , Consider the interpolating polynomial for f(x) =x² based on th points (0,0). (1,1) and (2,8). Find…

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Q: rove if the ff. arguments are valid using any formal proof of validity. vx, (P(x) v Q(x)) vx,…

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Q: Which of the following points is at a distance of 5V2 from the origin. * O (0,0) O (5,0) O (5,5) O…

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Q: Find the midpoint of (6, 7) and (14, 11). O (7, 18) О 20, 18) О 10, 10) (10, 9)

A: given points :(x1,y1)=( 6,7)(x2,y2)=(14,11) Midpoint = x1+x22,y1+y22

Q: R(s, t) = G(u(s, t), v(s, t)), where G, u, and vare differentiable, and the following applies. v(7,…

A: Given that

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: Suppose X₁ and X₂ are i.r.v. and come from gamma(2a, 2). Show that U = X₁ + X₂ comes from gamma(4a,…

A: Given that X1 and X2 are i.r.v. from a gamma distribution.want to show that U=X1+X2 comes from a…

Q: Given z=f(x, y), z = x(u, v), y=y(u, v), with z(7,5) = 5 and y(7,5)=3, calculate z, (7,5) in terms…

A: The given function is z=fx, y, x=xu, v, y=yu, v. The given table is fx7, 5=2 fy7, 5=a xu7, 5=2…

Q: Use the function to find (a) the image of v and (b) the preimage of w.

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Q: b) Use xo = 1, X₁ = 1.5, x₂ = 2 to find the second interpolating polynomial to 3 f(x) = 2x+1

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Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. 4 r(t) = (41²) ₁ +…

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Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

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Q: 1 s) Let f(x, y) = x¹y-²-5ry- ? (graye ! 'e' e7 In (2ry), find fzz, fyy, fry, and fyz. Sadda

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Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

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Q: Given f(x, y, z) = 7x − 7y² + 6z², x = √u + v, y = (u + w) In(v), z = 2 – v + 7w. Find and ди, ду of…

A: Firstly differentiate f with respect to x ,y ,z  and then differentiate  x , y , z with respect to…