Question

A coin is tossed twice. Consider the following events. A: Heads on the first toss. B:...

A coin is tossed twice. Consider the following events.

A: Heads on the first toss.

B: Heads on the second toss.

C: The two tosses come out the same.

(a) Show that A, B, C are pairwise independent but not independent.

(b) Show that C is independent of A and B but not of A ∩ B.

Math   Statistics-And-Probability   
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Answer #1

If a coin is tossed twice.

(H H), (H T), (T T), (T H) = 4 outcomes

A: Heads on the first toss. (H H), (H T)

B: Heads on the second test. (H H), (T H)

C: The two tosses come out the same. (H H) (T T)

a) A, B and C are pairwise independent if

Hence A,B and C are pairwise independent.

b) C is independent of only if

hence

Thus C is not independent of

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