Statistics Solutions

(Steps Shown) A box contains four balls, numbered 1 through 4. One ball is selected at random from this box. Let: X 1 = 1 if ball 1 or ball 2 is drawn, X 2 =

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

X 1 = 1 if ball 1 or ball 2 is drawn,

X 2 = 1 if ball 1 or ball 3 is drawn,

X 3 = 1 if ball 1 or ball 4 is drawn.

The Xi values are zero otherwise. Show that any two of the random variables X 1 , X 2 , and X 3 are independent but that the three together are not.

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