The marginal density functions of X and Y are and £x(x) = [** £x,y(x,y) dy = @F(x,∞) əx fy(y) = [*_ƒx,y(x, y)dx = ©F (∞, y) dy

Q: Which of the following is equivalent to S = {spring, summer, autumn, winter}?

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Q: Prove the following: 1. erfc(∞) = 0

A: Below we have given the definition of erf(x) and relationship between erf(x) and erfc(x).

Q: A. let w-e te Find W2

A: We can solve this using u/v rule

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A: Here given matrix is  A=111111111

Q: (A) In y

A: The detailed solution is as follows below:

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A: Let us provide justification and check whether both equations are equivalent or not

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A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

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Q: Section 2.2 as) Given: mく3 > m<4 a Prove FH is not I to EG H.

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Q: Let à . Find al.

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Q: and xe"y %3D For ay

A: To find out partial derivatives.

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A: Let us take the approach of the use of sets and logic to approach the solution to the given problem,…

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A: We eliminate the arbitrary function f from the given equation to form the required partial…

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Q: 5. If A = I then what is A?

A: Here given as A2=I Taking determinant both side A2=IA2=1A=±1 Thus A is non singular and inverse of A…

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Q: Given A = 03-2 00 1 compute et.

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Q: Evaluate the following E jOO) i() ())]

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Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

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A: Venn diagram are pictorial representations of mathematical or logical sets of data as closed curves…

Q: Prove That Cn) =nsh ツールがー

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Q: Prove or disprove that if (A U B) C (An B), then A = B

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Q: Prove the following: (a) If a, b, c e Z+ and a +b= c then (c, [a, b)) = (a,b). %3D

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