Find: fx,x(x, y) = { cay² 0≤x≤ 1,0 ≤8≤1 otherwise a) Constant c. b) P[X > Y], P[Y < X²]. c) P[min(X,Y) ≤ 1/2], P[max(X,Y) < 3/4]. d) Find the marginal PDFs fx(x) and fy(y). e) Are these random variables independent?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Let X and Y be continuous random variables with joint PDF

 

Find:
fx,x(x, y) = { cay² 0≤x≤ 1,0 ≤8≤1
otherwise
a) Constant c.
b) P[X > Y], P[Y < X²].
c) P[min(X,Y) ≤ 1/2], P[max(X,Y) < 3/4].
d) Find the marginal PDFs fx(x) and fy(y).
e) Are these random variables independent?
Transcribed Image Text:Find: fx,x(x, y) = { cay² 0≤x≤ 1,0 ≤8≤1 otherwise a) Constant c. b) P[X > Y], P[Y < X²]. c) P[min(X,Y) ≤ 1/2], P[max(X,Y) < 3/4]. d) Find the marginal PDFs fx(x) and fy(y). e) Are these random variables independent?
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