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: 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: Two students are named to present their work from a class of 12 students: 5 from electrical…

A: Total = 12 students Electrical = 5 students Telecommunication = 4 students  Computer = 3 students

Q: Please prove 2(b)(iv)>(v)

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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: 5. Determine the combination V x (Vf) given that X" + y"

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Q: Find an integer coefficient cubic that has x = 1 and x = 2+ /3 as zeros.

A: Given: The two zeros of a cubic polynomial are x=1 and x=2+3.

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Show that V spans P² where V = {1 + 2t + 2t², t + t², 1 − t²}

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Q: 3) a) Determine the linear Lagrange interpolation polynomial that passes through the points (-1, 2)…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Q4) a) Let , and 0, be two unbiased estimators of 0. Show that ô, = aô, +(1– a)ê,, 0sasl is an…

A: Q 4a) Here it is given that θ1^ and  θ2^are two unbaised estimater of θie E( θ1^)=E( θ2^)=θNow Here…

Q: Is Q closed over multiplication? (Y/N)

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Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: 6. (10pts) Determine whether you can find the interpolating polynomial p(t) = a, + a,t + a,r² for…

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Q: The set of polynomials {1, x² + 3x“, 2x² – 7x4} is a linearly independent set in P4.

A: NOTE: Due to time limit answer of 1 is given here, for other please ask in a different question.…

Q: let fAg be funcbions that sabis fy fla)= -4 A g la)=-9. find h'la) for: a) h(x) = 2f(x) c) h(x)= 10…

A: Since multiple sub parts ate asked, I am answering first 3 subparts.

Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

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Q: (3) Construct a linear spline interpolating (-1, 0), (0, 1), (1, 3).

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Q: Let X and Y be jointly cantinuous random variables with joint PDF is given: $ X,Y (x.y) =…

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Q: A2

A: Consider the matrix A is, A=0100 Apply the condition, A2 = O. 0100·0100=0000 The matrix A is…

Q: The product of 2x3 + 3x2 +1 and 2x2 + 4 in z5 [x]/ is: X^2+2 None 5x^2+ 5x +1 O 4x+1

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Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

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Q: Suppose that Cov(X, Y ) = 5. What is Cov(3X + 4, 9Y )?

A: Cov(X, Y ) = 5 & We have to find Cov(3X + 4, 9Y )

Q: Disprove: X={r1, 12} iff V, (z E X +x=VI=T2)

A: To do: Disprove the statement…

Q: 17. Use Theorem 4.7 to prove that Vx + 3 2 V3 + x/4 for

A: Let,

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…

Q: List all cosets of (([1]3, [2]6)) in Z3 × Ze

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Q: Let X be N(0, 1)and Y be N(0, 9) , with X and Y independent. Let Z 2X – 16Y, and let W = 3X3 + 4Y5…

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