a) Suppose that X and Y are two continuous random variables with the following joint density function ka30 (1 – y) ,0 < x < y <1 f(x, y) = , elsewhere Find the value of k that makes f(x, y) a valid joint density function.

a) Suppose that X and Y are two continuous random variables with the following joint density function ka30 (1 – y) ,0 < x < y <1 f(x, y) = , elsewhere Find the value of k that makes f(x, y) a valid joint density function.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 20E

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Question

a) Suppose that X and Y are two continuous random variables with the following joint density
function
kæ30 (1 – y) ,0 <x < y<1
f(x, y) =
,elsewhere
Find the value of k that makes f(x, y) a valid joint density function.
b) Let X and Y be jointly continuous random variables with the following joint density function
(1/32)æy ,0 < y <x < 4
f(x, y) =
, elsewhere
i. Find the marginal density function of X
ii. Are X and Y independent? Do a statistical calculation to support your response
iii. Find f(y|x)
iv. Determine P(X > 2)
v. Evaluate P(Y > X – 2)

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