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Let (X, Y) be a random vector with joint PMF given by »-(0-1) (12) (y − 1) = px,y (x, y) x+y if x = {1,2,...}, y = {2,3,...} otherwise (a) Verify that px,y(x, y) is a valid joint PMF. (b) Find the marginal PMFs of X and Y. Hint: You can answer this question without doing any additional summations! (c) Use your answer to part (b) to compute E[X] and E[Y]. Hint: You can answer this ques- tion without doing any additional summations! (d) Compute E[XY]. Hint: You can answer this question without doing any additional sum- mations! Just be sure to justify all of your work/steps.

Let (X, Y) be a random vector with joint PMF given by »-(0-1) (12) (y − 1) = px,y (x, y) x+y if x = {1,2,...}, y = {2,3,...} otherwise (a) Verify that px,y(x, y) is a valid joint PMF. (b) Find the marginal PMFs of X and Y. Hint: You can answer this question without doing any additional summations! (c) Use your answer to part (b) to compute E[X] and E[Y]. Hint: You can answer this ques- tion without doing any additional summations! (d) Compute E[XY]. Hint: You can answer this question without doing any additional sum- mations! Just be sure to justify all of your work/steps.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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 (X, Y) be a random vector with joint PMF given by x+y px,y (x, y) = = - 1) (¹²) if x € {1,2,...}, y = {2,3,...} otherwise (a) Verify that px,y(x, y) is a valid joint PMF. (b) Find the marginal PMFs of X and Y. Hint: You can answer this question without doing any additional summations! (c) Use your answer to part (b) to compute E[X] and E[Y]. Hint: You can answer this ques- tion without doing any additional summations! (d) Compute E[XY]. Hint: You can answer this question without doing any additional sum- mations! Just be sure to justify all of your work/steps.
Transcribed Image Text:Let (X, Y) be a random vector with joint PMF given by x+y px,y (x, y) = = - 1) (¹²) if x € {1,2,...}, y = {2,3,...} otherwise (a) Verify that px,y(x, y) is a valid joint PMF. (b) Find the marginal PMFs of X and Y. Hint: You can answer this question without doing any additional summations! (c) Use your answer to part (b) to compute E[X] and E[Y]. Hint: You can answer this ques- tion without doing any additional summations! (d) Compute E[XY]. Hint: You can answer this question without doing any additional sum- mations! Just be sure to justify all of your work/steps.
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