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Consider the following joint PMF: Px,y (x, y) 0 1 X -2 -1 1/12 0 1/3 0 0 Y +1 1/6 0 +2 0 1/6 1/12 1/12 1/12 (a) Determine the marginal PMFs Px(x) and Py(y). (b) Calculate E[X] and E[Y]. (c) Calculate P[X < Y]. (d) Determine the conditional PMF Px|y(x|y) and write it out as a table. (e) Calculate P[X > 1|Y = 2]. (f) Are X and Y independent? (g) Calculate E[2X – 3Y].

Consider the following joint PMF: Px,y (x, y) 0 1 X -2 -1 1/12 0 1/3 0 0 Y +1 1/6 0 +2 0 1/6 1/12 1/12 1/12 (a) Determine the marginal PMFs Px(x) and Py(y). (b) Calculate E[X] and E[Y]. (c) Calculate P[X < Y]. (d) Determine the conditional PMF Px|y(x|y) and write it out as a table. (e) Calculate P[X > 1|Y = 2]. (f) Are X and Y independent? (g) Calculate E[2X – 3Y].

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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Only d, e, f, g please!! Thank you!!

Consider the following joint PMF: Px,y(x, y) 0 1 2 X Y -2 -1 +2 1/12 0 1/3 1/6 0 1/12 1/12 1/12 +1 0 1/6 (a) Determine the marginal PMFs Px(x) and Py(y). (b) Calculate E[X] and E[Y]. (c) Calculate P[X < Y]. (d) Determine the conditional PMF Px|y(x|y) and write it out as a table. (e) Calculate P[X > 1|Y = 2]. (f) Are X and Y independent? (g) Calculate E[2X – 3Y].
Transcribed Image Text:Consider the following joint PMF: Px,y(x, y) 0 1 2 X Y -2 -1 +2 1/12 0 1/3 1/6 0 1/12 1/12 1/12 +1 0 1/6 (a) Determine the marginal PMFs Px(x) and Py(y). (b) Calculate E[X] and E[Y]. (c) Calculate P[X < Y]. (d) Determine the conditional PMF Px|y(x|y) and write it out as a table. (e) Calculate P[X > 1|Y = 2]. (f) Are X and Y independent? (g) Calculate E[2X – 3Y].
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