Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x,y) = {k(x+y), 0≤x≤y≤ı elsewhere Find: a) Show that the value of k = 2 so that f(x, y) is a joint pdf. b) the marginal of X and Y. c) the joint cumulative density function (CDF), F(x, y). d) the conditional pdf of Y given X. e) E(Y|X = -1)
Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x,y) = {k(x+y), 0≤x≤y≤ı elsewhere Find: a) Show that the value of k = 2 so that f(x, y) is a joint pdf. b) the marginal of X and Y. c) the joint cumulative density function (CDF), F(x, y). d) the conditional pdf of Y given X. e) E(Y|X = -1)
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
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![Let X and Y be continuous random variables with a joint probability density function (pdf) of
the form
f(x, y) =
={k(x+y), 0≤x≤y≤1
0,
elsewhere
Find:
a) Show that the value of k = 2 so that f(x, y) is a joint pdf.
b) the marginal of X and Y.
c) the joint cumulative density function (CDF), F(x, y).
d) the conditional pdf of Y given X.
e) E(YIX=-1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98045eb8-67c9-4c5f-b511-4afdd76e7951%2F6ea1fd43-1615-43b8-9ab8-c2ea48d2f950%2F35xrhik_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X and Y be continuous random variables with a joint probability density function (pdf) of
the form
f(x, y) =
={k(x+y), 0≤x≤y≤1
0,
elsewhere
Find:
a) Show that the value of k = 2 so that f(x, y) is a joint pdf.
b) the marginal of X and Y.
c) the joint cumulative density function (CDF), F(x, y).
d) the conditional pdf of Y given X.
e) E(YIX=-1)
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