# mutual independence implies pairwise independence show that the converse is not true. [duplicate]

We know:

Mutual Independence :

For $n‎\geq‎‎‎‎3$, random variables $X_1,X_2,...,X_n$ are mutually independent if $$p(x_1,x_2,...,x_n)=p(x_1)p(x_2)...p(x_n)$$ for all $x_1,x_2,...,x_n$.

Pairwise Independence :

For $n‎\geq‎‎‎‎3$, random variables $X_1,X_2,...,X_n$ are pairwise independent if $X_i,X_j$ are independent for all $1\leq i<j\leq n$.

Note that mutual independence implies pairwise independence.(Proof that mutual statistical independence implies pairwise independence) show that the converse is not true.

Personally, I think the answer is cleared with the definition of 'Conditional Independence', but any help is appreciated.

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Easiest example: Suppose three people are each tossing a fair coin. Consider the three events $(A,B)$ match, $(B,C)$ match, and $(A,C)$ match.