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Suppose that X is uniformly chosen from {1,2,3} and (Y | X = k) ~ Binomial(2, §). We have a 4-sided die, and paint X of its faces red, leaving the rest white; X is uniformly chosen from {1, 2, 3}. Then we roll the die twice, and let Y be the number of times a red face comes up. In other words, (Y | X = k) ~ Binomial(2, §). Give the following in the form of a table: (a) Pyx (ba), the conditional PMF of Y given X. (b) Pxy (a, b), the joint PMF of X and Y. (c) Pxy (a | b), the conditional PMF of X given Y. (d) Finally, explain what the X = 1, Y = 1 entry of your table in (c) means, in reference to the die with painted faces.

Suppose that X is uniformly chosen from {1,2,3} and (Y | X = k) ~ Binomial(2, §). We have a 4-sided die, and paint X of its faces red, leaving the rest white; X is uniformly chosen from {1, 2, 3}. Then we roll the die twice, and let Y be the number of times a red face comes up. In other words, (Y | X = k) ~ Binomial(2, §). Give the following in the form of a table: (a) Pyx (ba), the conditional PMF of Y given X. (b) Pxy (a, b), the joint PMF of X and Y. (c) Pxy (a | b), the conditional PMF of X given Y. (d) Finally, explain what the X = 1, Y = 1 entry of your table in (c) means, in reference to the die with painted faces.

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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3. Suppose that X is uniformly chosen from {1,2,3} and (Y | X = k) ~ Binomial(2, 4). We have a 4-sided die, and paint X of its faces red, leaving the rest white; X is uniformly chosen from {1, 2, 3}. Then we roll the die twice, and let Y be the number of times a red face comes up. In other words, (Y | X = k) ~ Binomial(2, 4). Give the following in the form of a table: (a) Pyx(ba), the conditional PMF of Y given X. (b) Pxy (a, b), the joint PMF of X and Y. (c) Pxy (a | b), the conditional PMF of X given Y. (d) Finally, explain what the X = 1, Y = 1 entry of your table in (c) means, in reference to the die with painted faces.
Transcribed Image Text:3. Suppose that X is uniformly chosen from {1,2,3} and (Y | X = k) ~ Binomial(2, 4). We have a 4-sided die, and paint X of its faces red, leaving the rest white; X is uniformly chosen from {1, 2, 3}. Then we roll the die twice, and let Y be the number of times a red face comes up. In other words, (Y | X = k) ~ Binomial(2, 4). Give the following in the form of a table: (a) Pyx(ba), the conditional PMF of Y given X. (b) Pxy (a, b), the joint PMF of X and Y. (c) Pxy (a | b), the conditional PMF of X given Y. (d) Finally, explain what the X = 1, Y = 1 entry of your table in (c) means, in reference to the die with painted faces.
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