Four bits are transmitted over a digital communications

QUESTION:

Go Tutorial Four bits are transmitted over a digital communications channel. Each bit is either distorted or received without distortion. Let \(Ai\) denote the event that the \(i\)th bit is distorted, \(i\)  = 1, …,4.

(a) Describe the sample space for this experiment.

(b) Are the \(Ai\)'s mutually exclusive? Describe the outcomes in each of the following events:

(c) \(A_{1}\)

(d) \(A_{1}{ }^{\prime}\)

(e) \(A_{1} \cap A_{2} \cap A_{3} \cap A_{4}\)

(f) \(\left(A_{1} \cap A_{2}\right) \cup\left(A_{3} \cap A_{4}\right)\)

Equation Transcription:

Text Transcription:

Ai

I

I

Ai

A_1

A_1’

A_1 cap A_2 cap A_3 cap A_4

(A_{1} cap A_{2}) cup(A_3 cap A_4)