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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.

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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Explan part c) in detail for me to understand. Thank you! 

1. Continuous random variables \(0 \leq X \leq 2\) and \(0 \leq Y \leq 2\) have joint probability density function \[ f_{X,Y}(x, y) = \frac{3x^2 + 4y}{32}. \] (a) Find and simplify a formula for the marginal density function \(f_X(x)\). (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.
Transcribed Image Text:1. Continuous random variables \(0 \leq X \leq 2\) and \(0 \leq Y \leq 2\) have joint probability density function \[ f_{X,Y}(x, y) = \frac{3x^2 + 4y}{32}. \] (a) Find and simplify a formula for the marginal density function \(f_X(x)\). (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.
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