the probabilities of the states of dependent systems X and Y are given by the table: (Xi, Yi) X1 Y1 0,05 0,3 Y2 0,15 0,2 Y3 0,25 0,05 1. Find private information I(y3, X) about system X contained in the message: "system Y is in state y3". 2. Find private information I(y2, x2) about the event "system X is in state x2" contained in the message: "system Y is in state y2". 3. Find complete information I(Y, X) about the system X contained in in the Y system.

the probabilities of the states of dependent systems X and Y are given by the table: (Xi, Yi) X1 Y1 0,05 0,3 Y2 0,15 0,2 Y3 0,25 0,05 1. Find private information I(y3, X) about system X contained in the message: "system Y is in state y3". 2. Find private information I(y2, x2) about the event "system X is in state x2" contained in the message: "system Y is in state y2". 3. Find complete information I(Y, X) about the system X contained in in the Y system.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 42E

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Question

the probabilities of the states of dependent systems X and Y are given by the table:

(Xi, Yi)	X1
Y1	0,05	0,3
Y2	0,15	0,2
Y3	0,25	0,05

1. Find private information I(y3, X) about system X contained in the
message: "system Y is in state y3".
2. Find private information I(y2, x2) about the event "system X is in state
x2" contained in the message: "system Y is in state y2".
3. Find complete information I(Y, X) about the system X contained in
in the Y system.

.N.B: the picture is the example of resolution for this exercice