Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R, by 3. fx.x (2,y) =0, { Ay exp(-y(x + )), if x > 0 and y > 0 otherwise. (i) Calculate the marginal density of Y. (ii) Let y > 0. Find the the conditional probability density function of X given Y = y. Interpret your answer. (iii) Calculate E[X|Y] and prove that E[X] = +oo. Hint: You can use without a proof that dy = +o.
Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R, by 3. fx.x (2,y) =0, { Ay exp(-y(x + )), if x > 0 and y > 0 otherwise. (i) Calculate the marginal density of Y. (ii) Let y > 0. Find the the conditional probability density function of X given Y = y. Interpret your answer. (iii) Calculate E[X|Y] and prove that E[X] = +oo. Hint: You can use without a proof that dy = +o.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R,
by
3.
fx,y(x, y) = { Ay exp(-y(x+ A)), if a 2 0 and y > 0
0,
otherwise.
(i) Calculate the marginal density of Y.
(ii) Let y > 0. Find the the conditional probability density function of X given Y = y.
Interpret your answer.
(iii) Calculate E[X|Y] and prove that E[X] = +oo.
Hint: You can use without a proof that
-dy = +oo.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64c507d3-89c0-41f2-a1b5-3b0fa8b93e01%2Fe72a4f7c-96e1-4aff-b5c3-221f4a78fa97%2Fo0ggn1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R,
by
3.
fx,y(x, y) = { Ay exp(-y(x+ A)), if a 2 0 and y > 0
0,
otherwise.
(i) Calculate the marginal density of Y.
(ii) Let y > 0. Find the the conditional probability density function of X given Y = y.
Interpret your answer.
(iii) Calculate E[X|Y] and prove that E[X] = +oo.
Hint: You can use without a proof that
-dy = +oo.
%3D
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