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A box contains four balls, numbered 1 through 4. One ball is selected at random from this box.

A box contains four balls, numbered 1 through 4. One ball is selected at random from this box. Let
X1 = 1 if ball 1 or ball 2 is drawn
X2 = 1 if ball 1 or ball 3 is drawn
X3 = 1 if ball 2 or ball 3 is drawn
and the X's are zero otherwise. Show that any two of the random variables X1, X2, and X3 are independent, but the three together are not.
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524952_STATS.docx

A box contains four balls, numbered 1 through 4. One ball is selected at random from this box.
Let
X1 = 1 if ball 1 or ball 2 is drawn
X2 = 1 if ball 1 or ball 3 is drawn
X3 = 1 if ball 2 or ball 3...

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