You are given a two dice with 4 sides each, with equal probability of landong on all sides. Dice one has values 1 - 4 and the second has values 5-8. The low-valued die (dice one) is rolled first. If you get a 1 or 2, then you roll the high-valued die (dice 2). If you get 3 or 4, you roll the low-valued die. X = value of the 1st roll Y = value of the 2nd roll Z = X + Y %3D Find H(X), H(Y), H(Z) Find H(Y|X) Find H(X,Y), H(X|Y) Find I (X;Y)

A First Course in Probability (10th Edition)
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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 are given a two dice with 4 sides each, with
equal probability of landong on all sides.
Dice one has values 1 - 4 and the second has values
5-8. The low-valued die (dice one) is rolled first. If you
get a 1 or 2, then you roll the high-valued die (dice 2).
If you get 3 or 4, you roll the low-valued die.
X= value of the 1st roll
Y = value of the 2nd roll
Z = X + Y
%3D
Find H(X), H(Y), H(Z)
Find H(Y|X)
Find H(X,Y), H(XIҮ)
Find I (X;Y)
Transcribed Image Text:You are given a two dice with 4 sides each, with equal probability of landong on all sides. Dice one has values 1 - 4 and the second has values 5-8. The low-valued die (dice one) is rolled first. If you get a 1 or 2, then you roll the high-valued die (dice 2). If you get 3 or 4, you roll the low-valued die. X= value of the 1st roll Y = value of the 2nd roll Z = X + Y %3D Find H(X), H(Y), H(Z) Find H(Y|X) Find H(X,Y), H(XIҮ) Find I (X;Y)
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