For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

Q: I| (2 + x²y)dA, R = [0, 1] × [–1, 1]

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Q: Find + ][a³dA where R = {(x, y) | 25x² +9y² ≤ 225} R

A: The given region is ellepse and we have to convert it into circle. Then we apply the integration.

Q: Suppose that A,B⊂S such that Pr[A|B]=3/7, Pr[A]=3/10 and Pr[B′]=13/20. What is Pr[B|A′]? Write as a…

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Q: Prove = cos for some x in (0, π/2).

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Q: Find J Smi x²dA where R = {(x, y) | 4x² + 16y² ≤ 64} R

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Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: (2) Prove that for all x, y € R, we have 8xy³ ≤ (2x + y³)².

A: A.M&gt;=G.M

Q: Suppose that A,B⊂S such that Pr[A|B]=25, Pr[A]=12 and Pr[B′]=12. What is Pr[B|A′]?

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Q: EXY] = E[X]E[Y]. 1}) and U~U({-1,1}) are independent. Let Y = XU. e uncorrelated. e not independent.

A: *Answer:

Q: Prove the following by using the Boolean identities: ((XY)Z) + (YZ) = YZ

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Q: [3 -2] Let A = 1 1 and define T: R² → R² by T(x) = Ax. Find |1 −1 -1 A. T ¹([₂]) = 2 [2].

A: Given: and define  by  we have to find

Q: Find a, b > 0 such that the following equality holds: {r €R : -a < br – 3 < v2} = [-3, 3).

A: Note the result : The set can be represented in interval form as .

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

A: Solution:-

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: Let I = S (8x + 10y + 4+ 12xy) dA where R = [0, 1] × [1,2]. R Find I

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