1. Continuous random variables 0 ≤ x ≤ 2 and 0 ≤ Y ≤ 2 have joint probability density function fx,y(x, y) = 3x² + 4y 32 (a) Find and simplify a formula for the marginal density function fx(x). (b) Compute E(XY). (c) Compute P(Y> 2X). Draw a picture of the full range and the event Y > 2X to help you understand this problem.

1. Continuous random variables 0 ≤ x ≤ 2 and 0 ≤ Y ≤ 2 have joint probability density function fx,y(x, y) = 3x² + 4y 32 (a) Find and simplify a formula for the marginal density function fx(x). (b) Compute E(XY). (c) Compute P(Y> 2X). Draw a picture of the full range and the event Y > 2X to help you understand this problem.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 23E

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For part c) let the double integral be dydx. Solve part c) into details, and help to draw the diagram and explain how to get the limits of integration. Thank you

1. Continuous random variables 0 ≤ X ≤ 2 and 0 ≤ Y ≤ 2 have joint probability density function
fx,y(x, y) =
3x² + 4y
32
(a) Find and simplify a formula for the marginal density function fx(x).
(b) Compute E(XY).
(c) Compute P(Y > 2X).
Draw a picture of the full range and the event Y > 2X to help you understand this problem.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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