Page 28 - Probability, Random Variables and Random Processes

PROBABILITY [CHAP 1

A, n A, A3 (7x2

Fig. 1-11

Thus, using axiom 3', we have

n
= lim z P(B,) = lirn P
n+m

Next, if (A,, n 2 1) is a decreasing sequence, then {A,, , n 2 1) is an increasing sequence. Hence, by Eq.
(1.73, we have

From Eq. (1.1 9),

) ) I
Thus, P Ai = lim P(An)
I-m
Using Eq. (1.25), Eq. (1.76) reduces to

Thus,

Combining Eqs. (1.75) and (1.77), we obtain Eq. (1.74).

EQUALLY LIKELY EVENTS

1.29. Consider a telegraph source generating two symbols, dots and dashes. We observed that the dots
were twice as likely to occur as the dashes. Find the probabilities of the dot's occurring and the
dash's occurring.