Let X = (Y, Z) be the fair dice roll with E(Y ) = {1, . . . , 6} with PY (y) = 1/6, and Z be an independent fair coin toss with E(Z) = {0, 1} and PZ(z) = 1/2. a) What is PX(x)? b) What is PX(Y) for the abstract event Y = {(1, 1),(2, 0)}? c) What is the probability of the event that z + y = 2? d) What is PZ|Y (1|6)?

Let X = (Y, Z) be the fair dice roll with E(Y ) = {1, . . . , 6} with PY (y) = 1/6, and Z be an independent fair coin toss with E(Z) = {0, 1} and PZ(z) = 1/2. a) What is PX(x)? b) What is PX(Y) for the abstract event Y = {(1, 1),(2, 0)}? c) What is the probability of the event that z + y = 2? d) What is PZ|Y (1|6)?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 35E

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Question

Let X = (Y, Z) be the fair dice roll with E(Y ) = {1, . . . , 6} with PY (y) = 1/6, and
Z be an independent fair coin toss with E(Z) = {0, 1} and PZ(z) = 1/2.
a) What is PX(x)?
b) What is PX(Y) for the abstract event Y = {(1, 1),(2, 0)}?
c) What is the probability of the event that z + y = 2?
d) What is PZ|Y (1|6)?

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