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Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0, 5] x [1,4]

Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0, 5] x [1,4]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0, 5] x [1,4]
Transcribed Image Text:Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0, 5] x [1,4]
Suppose X and Y are random variables with joint density function. f(x, y) = {0.16 [0.1e-(0.5x+0.2y) (a) Is f a joint density function? Yes O No if x ≥ 0, y ≥ 0 otherwise (b) Find P(Y ≥ 5). (Round your answer to four decimal places.) Find P(X ≤ 3, Y ≤ 4). (Round your answer to four decimal places.) (c) Find the expected value of X. Find the expected value of Y.
Transcribed Image Text:Suppose X and Y are random variables with joint density function. f(x, y) = {0.16 [0.1e-(0.5x+0.2y) (a) Is f a joint density function? Yes O No if x ≥ 0, y ≥ 0 otherwise (b) Find P(Y ≥ 5). (Round your answer to four decimal places.) Find P(X ≤ 3, Y ≤ 4). (Round your answer to four decimal places.) (c) Find the expected value of X. Find the expected value of Y.
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