You flip a fair coin twice. X is 2 if the first coin is heads and 4 if the first coin is tails. Y is 2 if the second coin is heads and 4 if the second coin is tails. Z is the product of X and Y where Z=XY. a) Are X and Y independently distributed? b) Are Z and Y independent?

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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You flip a fair coin twice. X is 2 if the first coin
is heads and 4 if the first coin is tails. Y is 2 if
the second coin is heads and 4 if the second
coin is tails. Z is the product of X and Y where
Z=XY.
a) Are X and Y independently distributed?
b) Are Z and Y independent?
Transcribed Image Text:You flip a fair coin twice. X is 2 if the first coin is heads and 4 if the first coin is tails. Y is 2 if the second coin is heads and 4 if the second coin is tails. Z is the product of X and Y where Z=XY. a) Are X and Y independently distributed? b) Are Z and Y independent?
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