Consider the following random experiment: first, X is chosen uniformly at random from the set {1,2,3}. Then, X fair coins are flipped, and we let Y be the number of heads. In other words, when X = x, we have Y~ · Binomial(x, ½). Fill in the branching diagram to the left with the probabilities of taking each fork, and the final probabilities of each endpoint. Then, use this to fill in the table of the joint PMF of X and Y on the right. Start Py (0) = X = 1 X = 2 X = 3 Find Pr[X = Y]. Y = 0 = = Y = 0 Y = 1 Y=2 Y = 0 Y = 1 Y = 2 Y = 3 Find the (marginal) PMF of Y. Py(1) Py (2) Y = 0 Y = 1 Y = 2 Y = 3 X = 1 X = 2 X=3 Py (3)
Consider the following random experiment: first, X is chosen uniformly at random from the set {1,2,3}. Then, X fair coins are flipped, and we let Y be the number of heads. In other words, when X = x, we have Y~ · Binomial(x, ½). Fill in the branching diagram to the left with the probabilities of taking each fork, and the final probabilities of each endpoint. Then, use this to fill in the table of the joint PMF of X and Y on the right. Start Py (0) = X = 1 X = 2 X = 3 Find Pr[X = Y]. Y = 0 = = Y = 0 Y = 1 Y=2 Y = 0 Y = 1 Y = 2 Y = 3 Find the (marginal) PMF of Y. Py(1) Py (2) Y = 0 Y = 1 Y = 2 Y = 3 X = 1 X = 2 X=3 Py (3)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![Consider the following random experiment: first, X is chosen uniformly at random from the set
{1,2,3}. Then, X fair coins are flipped, and we let Y be the number of heads. In other words,
when X = x, we have Y Binomial(x, ).
Fill in the branching diagram to the left with the probabilities of taking each fork, and
the final probabilities of each endpoint. Then, use this to fill in the table of the joint PMF of X
and Y on the right.
Start
~
Py(0) =
=
X = = 1
X = 2
X = 3
Find Pr[X = Y].
Y = 0
Y = 1
Y = 0
Y = 1
Y = 2
Y = 0
Y = 1
Y = 2
Y:
= 3
Find the (marginal) PMF of Y.
Py(1) =
=
Y = 0
Y = 1
Y
Y
Py(2)
=
=
=
23
2
3
X = 1 X = 2 X=3
Py(3) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd3c2ff7-376d-42ab-9375-076cf278b626%2F20244667-dfdf-4bee-95fd-4e064ebf722e%2F3f0skz_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following random experiment: first, X is chosen uniformly at random from the set
{1,2,3}. Then, X fair coins are flipped, and we let Y be the number of heads. In other words,
when X = x, we have Y Binomial(x, ).
Fill in the branching diagram to the left with the probabilities of taking each fork, and
the final probabilities of each endpoint. Then, use this to fill in the table of the joint PMF of X
and Y on the right.
Start
~
Py(0) =
=
X = = 1
X = 2
X = 3
Find Pr[X = Y].
Y = 0
Y = 1
Y = 0
Y = 1
Y = 2
Y = 0
Y = 1
Y = 2
Y:
= 3
Find the (marginal) PMF of Y.
Py(1) =
=
Y = 0
Y = 1
Y
Y
Py(2)
=
=
=
23
2
3
X = 1 X = 2 X=3
Py(3) =
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