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?
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
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Let X and Y be continuous random variables with joint
![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F099a9854-7cc3-46b9-a37c-ec0486b4a12a%2Fdd5fad2b-0036-403b-b224-6a727736fac6%2F6sn68yo_processed.png&w=3840&q=75)
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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