Question

1. A block of information is transmitted repeatedly over a noisy channel until an error-free block arrives at the receiver. The number of required transmissions is recorded, so that the sample space is S = {1, 2, 3, 4, …}. (a) Write out the outcomes in the event A = “the number of transmissions required is an even number.”

(b) Write out the outcomes in the event B = “the number of transmissions required is a multiple of 3.”

(c) Write out the outcomes in the event C = “six or fewer transmissions are required.”

(d) Write out the events A ∩ B and A ∩ B ∩ C.

Answer 1

(a)

the outcomes in the event A = “the number of transmissions required is an even number.

A = { 2, 4, 6,...}

(b)

the outcomes in the event B = “the number of transmissions required is a multiple of 3.”

B = { 3, 6, 9, ...}

(c)

the outcomes in the event C = “six or fewer transmissions are required.”

C = { 1, 2, 3 4, 5, 6}

(d)

(i)

= { 6, 12, 18,....}

Explanaton:

A is multiples of 2.

B is multiples of .3.

So,

is multiples of 2 X3 = 6

(ii)

= { 6 }