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.
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ceae03-ce82-43df-b816-3449c4a6aa24%2F85955e84-f244-4fe2-ba30-f7ca1f21abfd%2F5774zq_processed.png&w=3840&q=75)
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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