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

Four bits are transmitted over a digital communications channel. Each bit is either distorted or received without distortion. Let
A_i
denote the event that the
ith bit is distorted,
i
= 1, p , 4.

(a) Describe the sample space for this experiment.

(b) Are the
A_i
’s mutually exclusive?

Describe the outcomes in each of the following events:

(c) A₁

(d) A₁’

(e) A₁
∩ A₂
∩ A₃
∩ A₄

(f) (A₁
∩ A₂
) ∪ (A₃
∩ A₄)