6.1.

Using the axioms of probability, prove Eq. (6.4).

6.2.

Verify Eq. (6.5).

6.3.

Verify Eq. (6.6).

6.4.

Verify Eq. (6.8).

6.5.

Let P( A) = 0.9 and P( B) = 0.8. Show that P( A ? B) ? 0.7.

6.6.

Show that

6.7.

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

6.8.

Show that P( A B) defined by Eq. (6.16) satisfies the three axioms of a probability, that is,

( a) P( A B) ? 0, ( b) P( S B) = 1, and ( c) P( A ? C B) = P( A B) + P( C B), if A ? C =

6.9.

Find P( A B) if ( a) A ? B = , ( b) A ? B, and ( c) B ? A.

6.10.

Show that if P( A B) > P( A), then P( B A) > P( B).

6.11.

Let A and B be events in a sample space S. Show that if A and B are...